We study Hamilton-Jacobi equations on networks in the case where Hamiltonians are quasi-convex with respect to the gradient variable and can be discontinuous with respect to the space variable at vertices. First, we prove that imposing a general vertex condition is equivalent to imposing a specific one which only depends on Hamiltonians and an additional free parameter, the flux limiter. Second, a general method for proving comparison principles is introduced. This method consists in constructing a vertex test function to be used in the doubling variable approach. With such a theory and such a method in hand, we present various applications, among which a very general existence and uniqueness result for quasi-convex Hamilton-Jacobi equations on networks.
{"title":"Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networks","authors":"C. Imbert, R. Monneau","doi":"10.24033/ASENS.2323","DOIUrl":"https://doi.org/10.24033/ASENS.2323","url":null,"abstract":"We study Hamilton-Jacobi equations on networks in the case where Hamiltonians are quasi-convex with respect to the gradient variable and can be discontinuous with respect to the space variable at vertices. First, we prove that imposing a general vertex condition is equivalent to imposing a specific one which only depends on Hamiltonians and an additional free parameter, the flux limiter. Second, a general method for proving comparison principles is introduced. This method consists in constructing a vertex test function to be used in the doubling variable approach. With such a theory and such a method in hand, we present various applications, among which a very general existence and uniqueness result for quasi-convex Hamilton-Jacobi equations on networks.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"693 1","pages":"357-448"},"PeriodicalIF":1.9,"publicationDate":"2013-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81795429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Varieties of minimal rational tangents of codimension 1","authors":"Jun-Muk Hwang","doi":"10.24033/ASENS.2197","DOIUrl":"https://doi.org/10.24033/ASENS.2197","url":null,"abstract":"","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"76 1","pages":"629-649"},"PeriodicalIF":1.9,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76830104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Erratum à «Sur une conjecture de Kottwitz au bord»","authors":"B. Stroh","doi":"10.24033/ASENS.2209","DOIUrl":"https://doi.org/10.24033/ASENS.2209","url":null,"abstract":"","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"115 1","pages":"1023-1024"},"PeriodicalIF":1.9,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78726096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The notations adopted are those of [Per11]. Proposition 5.11 of [Per11] states that if a torsion-free hyperbolic group A admits a cyclic JSJ-like decomposition Λ, and a non injective morphism f : A → A which restricts to conjugation on each non surface type vertex group, and sends surface type vertex groups to non abelian images, then there is a retraction r : A→ A′ which gives A a structure of hyperbolic floor over A′. Unfortunately, we realised that Proposition 5.11 fails to hold in a few exceptional low complexity cases. The natural modification to overcome this mistake is to proceed to a slight generalization of the notion of hyperbolic floors and hyperbolic towers, which we present in Section 1. As we will see in Section 2, however, this does not affect Theorem 1.2, the main result of the paper. Moreover, Theorem 1.2 is the only result which directly uses Proposition 5.11 in its proof. For a corrected version of the paper, see [Per09]. We sincerely apologize for any confusion caused by this mistake.
{"title":"Erratum to: “Elementary embeddings in torsion-free hyperbolic groups”","authors":"Chloé Perin","doi":"10.24033/ASENS.2203","DOIUrl":"https://doi.org/10.24033/ASENS.2203","url":null,"abstract":"The notations adopted are those of [Per11]. Proposition 5.11 of [Per11] states that if a torsion-free hyperbolic group A admits a cyclic JSJ-like decomposition Λ, and a non injective morphism f : A → A which restricts to conjugation on each non surface type vertex group, and sends surface type vertex groups to non abelian images, then there is a retraction r : A→ A′ which gives A a structure of hyperbolic floor over A′. Unfortunately, we realised that Proposition 5.11 fails to hold in a few exceptional low complexity cases. The natural modification to overcome this mistake is to proceed to a slight generalization of the notion of hyperbolic floors and hyperbolic towers, which we present in Section 1. As we will see in Section 2, however, this does not affect Theorem 1.2, the main result of the paper. Moreover, Theorem 1.2 is the only result which directly uses Proposition 5.11 in its proof. For a corrected version of the paper, see [Per09]. We sincerely apologize for any confusion caused by this mistake.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"23 1","pages":"851-856"},"PeriodicalIF":1.9,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85949676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It is proved that the Green's function of a symmetric finite range random walk on a co-compact Fuchsian group decays exponentially in distance at the radius of convergence R. It is also shownthatAncona'sinequalitiesextendtoR,andthereforethattheMartinboundaryforR-potentials coincides with the natural geometric boundary S 1 , and that the Martin kernel is uniformly Holder continuous. Finally, this implies a local limit theorem for the transition probabilities: in the aperiodic case, p n (x;y) Cx;yR n n 3=2 .
证明了在共紧Fuchsian群上对称有限范围随机游动的Green函数在收敛半径r处随距离呈指数衰减，并证明了ancona不等式等于extendtor，因此r势的martinboundary与自然几何边界s1重合，并且证明了Martin核是一致Holder连续的。最后，给出了跃迁概率的局部极限定理:在非周期情况下，np (x;y) Cx;yR n n 3=2。
{"title":"Random walks on co-compact fuchsian groups","authors":"S. Gouëzel, S. Lalley","doi":"10.24033/ASENS.2186","DOIUrl":"https://doi.org/10.24033/ASENS.2186","url":null,"abstract":"It is proved that the Green's function of a symmetric finite range random walk on a co-compact Fuchsian group decays exponentially in distance at the radius of convergence R. It is also shownthatAncona'sinequalitiesextendtoR,andthereforethattheMartinboundaryforR-potentials coincides with the natural geometric boundary S 1 , and that the Martin kernel is uniformly Holder continuous. Finally, this implies a local limit theorem for the transition probabilities: in the aperiodic case, p n (x;y) Cx;yR n n 3=2 .","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"1 1","pages":"131-175"},"PeriodicalIF":1.9,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72729769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We give a direct proof for the analyticity of the Stokes semigroup in spaces of bounded functions. This was recently proved by an indirect argument by the first and second authors for a class of domains called strictly admissible domains including bounded and exterior domains. Invoking the strictly admissibility, our approach is based on an adjustment of a standard resolvent estimate method for general elliptic operators introduced by K. Masuda (1972) and H. B. Stewart (1974). The resolvent approach in particular clarifies the sectorial region, Re z > 0 for z ∈ C for which the Stokes semigroup has an analytic continuation in spaces of bounded functions.
给出了有界函数空间中Stokes半群的可解析性的一个直接证明。最近，第一和第二作者通过间接论证证明了这一点，证明了一类称为严格可容许域的域包括有界域和外域。引用严格容许性，我们的方法是基于K. Masuda(1972)和H. B. Stewart(1974)引入的一般椭圆算子的标准解析估计方法的调整。特别地，解解法澄清了对于z∈C, Stokes半群在有界函数空间中具有解析延拓的扇形区域Re z > 0。
{"title":"Stokes Resolvent Estimates in Spaces of Bounded Functions","authors":"K. Abe, Y. Giga, Matthias Hieber","doi":"10.24033/ASENS.2251","DOIUrl":"https://doi.org/10.24033/ASENS.2251","url":null,"abstract":"We give a direct proof for the analyticity of the Stokes semigroup in spaces of bounded functions. This was recently proved by an indirect argument by the first and second authors for a class of domains called strictly admissible domains including bounded and exterior domains. Invoking the strictly admissibility, our approach is based on an adjustment of a standard resolvent estimate method for general elliptic operators introduced by K. Masuda (1972) and H. B. Stewart (1974). The resolvent approach in particular clarifies the sectorial region, Re z > 0 for z ∈ C for which the Stokes semigroup has an analytic continuation in spaces of bounded functions.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"8 1","pages":"537-559"},"PeriodicalIF":1.9,"publicationDate":"2012-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89752526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Semi-positivity in positive characteristics","authors":"Z. Patakfalvi","doi":"10.24033/ASENS.2232","DOIUrl":"https://doi.org/10.24033/ASENS.2232","url":null,"abstract":"Reference EPFL-ARTICLE-231106doi:10.24033/asens.2232 URL: http://dx.doi.org/10.24033/asens.2232 Record created on 2017-09-19, modified on 2017-10-02","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"38 1","pages":"991-1025"},"PeriodicalIF":1.9,"publicationDate":"2012-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78134610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Resume. — Soit F un corps totalement reel, v une place de F non ramifiee di- visant p et ρ : Gal(Q/F) → GL2(Fp) une representation continue irreductible dont la restriction ρ| Gal(Fv/Fv) est reductible et suffisamment generique. Siρ est modu- laire (et satisfait quelques conditions techniques faibles), nous montrons comment retrouver l'extension correspondante entre les deux caracteres de Gal(Fv/Fv) en terme de l'action de GL2(Fv) sur la cohomologie modulo p. Abstract. — Let F be a totally real field, v an unramified place of F dividing p and ρ : Gal(Q/F) → GL2(Fp) a continuous irreducible representation such that ρ| Gal(Fv/Fv) is reducible and sufficiently generic. Ifρ is modular (and satisfies some weak technical assumptions), we show how to recover the corresponding extension between the two characters of Gal(Fv/Fv) in terms of the action of GL2(Fv) on the cohomology mod p.
{"title":"FORMES MODULAIRES DE HILBERT MODULO p ET VALEURS D'EXTENSIONS GALOISIENNES","authors":"C. Breuil, Fred Diamond","doi":"10.24033/asens.2230","DOIUrl":"https://doi.org/10.24033/asens.2230","url":null,"abstract":"Resume. — Soit F un corps totalement reel, v une place de F non ramifiee di- visant p et ρ : Gal(Q/F) → GL2(Fp) une representation continue irreductible dont la restriction ρ| Gal(Fv/Fv) est reductible et suffisamment generique. Siρ est modu- laire (et satisfait quelques conditions techniques faibles), nous montrons comment retrouver l'extension correspondante entre les deux caracteres de Gal(Fv/Fv) en terme de l'action de GL2(Fv) sur la cohomologie modulo p. Abstract. — Let F be a totally real field, v an unramified place of F dividing p and ρ : Gal(Q/F) → GL2(Fp) a continuous irreducible representation such that ρ| Gal(Fv/Fv) is reducible and sufficiently generic. Ifρ is modular (and satisfies some weak technical assumptions), we show how to recover the corresponding extension between the two characters of Gal(Fv/Fv) in terms of the action of GL2(Fv) on the cohomology mod p.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"51 1","pages":"905-974"},"PeriodicalIF":1.9,"publicationDate":"2012-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73239892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
O. Guès, G. Métivier, Mark E. Williams, K. Zumbrun
We initiate the study of noncharacteristic boundary layers in hyperbolic-parabolic problems with Neumann boundary conditions. More generally, we study boundary layers with mixed Dirichlet{Neumann boundary conditions where the number of Dirichlet conditions is fewer than the number of hyperbolic characteristic modes entering the domain, that is, the number of boundary conditions needed to specify an outer hyperbolic solution. We have shown previously that this situation prevents the usual WKB approximation involving an outer solution with pure Dirichlet conditions. It also rules out the usual maximal estimates for the linearization of the hyperbolic-parabolic problem about the boundary layer. Here we show that for linear, constant-coecien t, hyperbolic-parabolic problems one obtains a reduced hyperbolic problem satisfying Neumann or mixed Dirichlet{Neumann rather than Dirichlet boundary conditions. When this hyperbolic problem can be solved, a unique formal boundary-layer expansion can be constructed. In the extreme case of pure Neumann conditions and totally incoming characteristics, we carry out a full analysis of the quasilinear case, obtaining a boundary-layer approximation to all orders with a rigorous error analysis. As a corollary we characterize the small viscosity limit for this problem. The analysis shows that although the associated linearized hyperbolic and hyperbolic{parabolic problems do not satisfy the usual maximal estimates for Dirichlet conditions, they do satisfy analogous versions with losses. Couches limites visqueuses pour des syst emes hyperboliques{paraboliques avec condition aux limites de Neumann
{"title":"Viscous boundary layers in hyperbolic-parabolic systems with Neumann boundary conditions","authors":"O. Guès, G. Métivier, Mark E. Williams, K. Zumbrun","doi":"10.24033/ASENS.2213","DOIUrl":"https://doi.org/10.24033/ASENS.2213","url":null,"abstract":"We initiate the study of noncharacteristic boundary layers in hyperbolic-parabolic problems with Neumann boundary conditions. More generally, we study boundary layers with mixed Dirichlet{Neumann boundary conditions where the number of Dirichlet conditions is fewer than the number of hyperbolic characteristic modes entering the domain, that is, the number of boundary conditions needed to specify an outer hyperbolic solution. We have shown previously that this situation prevents the usual WKB approximation involving an outer solution with pure Dirichlet conditions. It also rules out the usual maximal estimates for the linearization of the hyperbolic-parabolic problem about the boundary layer. Here we show that for linear, constant-coecien t, hyperbolic-parabolic problems one obtains a reduced hyperbolic problem satisfying Neumann or mixed Dirichlet{Neumann rather than Dirichlet boundary conditions. When this hyperbolic problem can be solved, a unique formal boundary-layer expansion can be constructed. In the extreme case of pure Neumann conditions and totally incoming characteristics, we carry out a full analysis of the quasilinear case, obtaining a boundary-layer approximation to all orders with a rigorous error analysis. As a corollary we characterize the small viscosity limit for this problem. The analysis shows that although the associated linearized hyperbolic and hyperbolic{parabolic problems do not satisfy the usual maximal estimates for Dirichlet conditions, they do satisfy analogous versions with losses. Couches limites visqueuses pour des syst emes hyperboliques{paraboliques avec condition aux limites de Neumann","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"4 1","pages":"181-243"},"PeriodicalIF":1.9,"publicationDate":"2012-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76054984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We construct a variant of Karoubi's relative Chern character for smooth varieties over C and prove a comparison result with Beilinson's regulator with values in Deligne-Beilinson cohomology. As a corollary we obtain a new proof of Burgos' Theorem that for number fields Borel's regulator is twice Beilinson's regulator.
{"title":"Karoubi's relative Chern character and Beilinson's regulator","authors":"Georg Tamme","doi":"10.24033/ASENS.2174","DOIUrl":"https://doi.org/10.24033/ASENS.2174","url":null,"abstract":"We construct a variant of Karoubi's relative Chern character for smooth varieties over C and prove a comparison result with Beilinson's regulator with values in Deligne-Beilinson cohomology. As a corollary we obtain a new proof of Burgos' Theorem that for number fields Borel's regulator is twice Beilinson's regulator.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"84 2 1","pages":"601-636"},"PeriodicalIF":1.9,"publicationDate":"2012-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89605228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：