Pub Date : 2022-01-01DOI: 10.1512/iumj.2022.71.8774
D. Wise
{"title":"Criteria for the vanishing of H_2^(2)","authors":"D. Wise","doi":"10.1512/iumj.2022.71.8774","DOIUrl":"https://doi.org/10.1512/iumj.2022.71.8774","url":null,"abstract":"","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66764776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.1512/iumj.2022.71.8947
Vicentiu D. Rădulescu, Chao Zhang
We establish a new Campanato type estimate for the weak solutions of a class of multi-phase problems. The problem under consideration is characterized by the fact that both ellipticity and growth switch between three different types of polynomial according to the position, which describes a feature of strongly anisotropic materials. The results obtained in this paper are different from the BMO type estimates for the usual p-Laplacian equation due to DiBenedetto and Manfredi. The content of this paper is in close relationship with the recent pioneering contributions of Marcellini and Mingione in the qualitative analysis of multi-phase problems.
{"title":"Gradient estimates for multi-phase problems in Campanato spaces","authors":"Vicentiu D. Rădulescu, Chao Zhang","doi":"10.1512/iumj.2022.71.8947","DOIUrl":"https://doi.org/10.1512/iumj.2022.71.8947","url":null,"abstract":"We establish a new Campanato type estimate for the weak solutions of a class of multi-phase problems. The problem under consideration is characterized by the fact that both ellipticity and growth switch between three different types of polynomial according to the position, which describes a feature of strongly anisotropic materials. The results obtained in this paper are different from the BMO type estimates for the usual p-Laplacian equation due to DiBenedetto and Manfredi. The content of this paper is in close relationship with the recent pioneering contributions of Marcellini and Mingione in the qualitative analysis of multi-phase problems.","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66765230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.1512/iumj.2022.71.8881
G. Figueiredo, M. Pimenta
In this work we use two different methods to get nodal solutions to quasilinear elliptic problems involving the 1−Laplacian operator. In the first one, we develop an approach based on a minimization of the energy functional associated to a problem involving the 1−Laplacian operator in R , on a subset of the Nehari set which contains just sign-changing functions. In the second part we obtain a nodal solution to a quasilinear elliptic problem involving the 1−Laplacian operator in a bounded domain, through a thorough analysis of the sequence of solutions of the p−Laplacian problem associated to it, as p → 1. In both cases, several technical difficulties appear in comparison with the related results involving signed solutions.
{"title":"Nodal solutions to quasilinear elliptic problems involving the 1-Laplacian operator via variational and approximation methods","authors":"G. Figueiredo, M. Pimenta","doi":"10.1512/iumj.2022.71.8881","DOIUrl":"https://doi.org/10.1512/iumj.2022.71.8881","url":null,"abstract":"In this work we use two different methods to get nodal solutions to quasilinear elliptic problems involving the 1−Laplacian operator. In the first one, we develop an approach based on a minimization of the energy functional associated to a problem involving the 1−Laplacian operator in R , on a subset of the Nehari set which contains just sign-changing functions. In the second part we obtain a nodal solution to a quasilinear elliptic problem involving the 1−Laplacian operator in a bounded domain, through a thorough analysis of the sequence of solutions of the p−Laplacian problem associated to it, as p → 1. In both cases, several technical difficulties appear in comparison with the related results involving signed solutions.","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66765262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.1512/iumj.2022.71.8965
Guangyi Hong, Hongyun Peng, Changjiang Zhu
In this paper, we are concerned with the motion of gas-kick flow in oil wells for the extreme case that the pressure is largely dictated by the surrounding reservoir pressure. Formally, the model can be obtained by taking the relaxation limit of a two-phase compressible gas-liquid model with a pressure-dependent well-reservoir interaction term. Under suitable smallness assumptions upon the initial data, the global existence as well as the uniqueness of strong solutions to the model is investigated by using the energy method. Besides, the large-time behavior of the solution is also studied. Our results generalize the ones in [18, S. Solem and S. Evje, Z. Angew. Math. Phys., 68 (2017), pp. Art. 23].
本文研究了在压力很大程度上取决于周围储层压力的极端情况下，油井中气涌流动的运动。在形式上，该模型可以通过取具有压力相关的井-储相互作用项的两相可压缩气-液模型的松弛极限得到。在初始数据较小的假设条件下，利用能量法研究了模型强解的全局存在性和唯一性。此外，还研究了该解的大时态。我们的结果推广了[18]S. Solem和S. Evje, Z. Angew的结果。数学。理论物理。， 68(2017)，第23条]。
{"title":"The relaxation limit of a compressible gas-liquid model with well-reservoir interaction","authors":"Guangyi Hong, Hongyun Peng, Changjiang Zhu","doi":"10.1512/iumj.2022.71.8965","DOIUrl":"https://doi.org/10.1512/iumj.2022.71.8965","url":null,"abstract":"In this paper, we are concerned with the motion of gas-kick flow in oil wells for the extreme case that the pressure is largely dictated by the surrounding reservoir pressure. Formally, the model can be obtained by taking the relaxation limit of a two-phase compressible gas-liquid model with a pressure-dependent well-reservoir interaction term. Under suitable smallness assumptions upon the initial data, the global existence as well as the uniqueness of strong solutions to the model is investigated by using the energy method. Besides, the large-time behavior of the solution is also studied. Our results generalize the ones in [18, S. Solem and S. Evje, Z. Angew. Math. Phys., 68 (2017), pp. Art. 23].","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66765780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.1512/IUMJ.2010.59.3935
T. Giorgi, R. G. Smits
We show that the reciprocal of the principal eigenvalue of some operators is comparable to the supremum of the solution to associated generalized torsion problems or the expected exit time for stochastic processes. As a result, we extend estimates, known for the Laplacian on simply connected two-dimensional domains, to general n-dimensional domains, to symmetric stable processes and to the p-Laplacian. Our proofs rely on probabilistic estimates and interpretations of the eigenvalues and the torsion functions.
{"title":"Errata: Principal eigenvalue estimates via the supremum of torsion","authors":"T. Giorgi, R. G. Smits","doi":"10.1512/IUMJ.2010.59.3935","DOIUrl":"https://doi.org/10.1512/IUMJ.2010.59.3935","url":null,"abstract":"We show that the reciprocal of the principal eigenvalue of some operators is comparable to the supremum of the solution to associated generalized torsion problems or the expected exit time for stochastic processes. As a result, we extend estimates, known for the Laplacian on simply connected two-dimensional domains, to general n-dimensional domains, to symmetric stable processes and to the p-Laplacian. Our proofs rely on probabilistic estimates and interpretations of the eigenvalues and the torsion functions.","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1512/IUMJ.2010.59.3935","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66895150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-06DOI: 10.1512/iumj.2022.71.9628
Kasia Jankiewicz, D. Wise
We give a simplified approach to the cubulation of small-cancellation quotients of free products of cubulated groups. We construct fundamental groups of compact nonpositively curved cube complexes that do not virtually split.
{"title":"Cubulating small cancellation free products","authors":"Kasia Jankiewicz, D. Wise","doi":"10.1512/iumj.2022.71.9628","DOIUrl":"https://doi.org/10.1512/iumj.2022.71.9628","url":null,"abstract":"We give a simplified approach to the cubulation of small-cancellation quotients of free products of cubulated groups. We construct fundamental groups of compact nonpositively curved cube complexes that do not virtually split.","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45494967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-04DOI: 10.1512/iumj.2022.71.9523
D. W. V. Wyk, Dana P. Williams
We study the topology of the primitive ideal space of groupoid C∗algebras for groupoids with abelian isotropy. Our results include the known results for action groupoids with abelain stabilizers. Furthermore, we obtain complete results when the isotropy map is continuous except for jump discontinuities, and also when G is a unit space fixing extension of a proper groupoid by an abelain group bundle. We hope that our methods will be a springboard to further results of this type.
{"title":"The primitive ideal space of groupoid C^*-algebras for groupoids with Abelian isotropy","authors":"D. W. V. Wyk, Dana P. Williams","doi":"10.1512/iumj.2022.71.9523","DOIUrl":"https://doi.org/10.1512/iumj.2022.71.9523","url":null,"abstract":"We study the topology of the primitive ideal space of groupoid C∗algebras for groupoids with abelian isotropy. Our results include the known results for action groupoids with abelain stabilizers. Furthermore, we obtain complete results when the isotropy map is continuous except for jump discontinuities, and also when G is a unit space fixing extension of a proper groupoid by an abelain group bundle. We hope that our methods will be a springboard to further results of this type.","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47944358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-23DOI: 10.1512/iumj.2023.72.9330
M. Conti, L. Liverani, V. Pata
We consider the MGT equation with memory $$partial_{ttt} u + alpha partial_{tt} u - beta Delta partial_{t} u - gammaDelta u + int_{0}^{t}g(s) Delta u(t-s) ds = 0.$$ We prove an existence and uniqueness result removing the convexity assumption on the convolution kernel $g$, usually adopted in the literature. In the subcritical case $alphabeta>gamma$, we establish the exponential decay of the energy, without leaning on the classical differential inequality involving $g$ and its derivative $g'$, namely, $$g'+delta gleq 0,quaddelta>0,$$ but only asking that $g$ vanishes exponentially fast.
我们考虑有内存的MGT方程$$partial_{ttt} u + alpha partial_{tt} u - beta Delta partial_{t} u - gammaDelta u + int_{0}^{t}g(s) Delta u(t-s) ds = 0.$$我们证明了一个存在唯一性结果，消除了文献中通常采用的卷积核的凸性假设$g$。在次临界情况$alphabeta>gamma$中，我们建立了能量的指数衰减，而不依赖于涉及$g$及其导数$g'$的经典微分不等式，即$$g'+delta gleq 0,quaddelta>0,$$，但只要求$g$以指数速度消失。
{"title":"On the Moore-Gibson-Thompson equation with memory with nonconvex kernels","authors":"M. Conti, L. Liverani, V. Pata","doi":"10.1512/iumj.2023.72.9330","DOIUrl":"https://doi.org/10.1512/iumj.2023.72.9330","url":null,"abstract":"We consider the MGT equation with memory $$partial_{ttt} u + alpha partial_{tt} u - beta Delta partial_{t} u - gammaDelta u + int_{0}^{t}g(s) Delta u(t-s) ds = 0.$$ We prove an existence and uniqueness result removing the convexity assumption on the convolution kernel $g$, usually adopted in the literature. In the subcritical case $alphabeta>gamma$, we establish the exponential decay of the energy, without leaning on the classical differential inequality involving $g$ and its derivative $g'$, namely, $$g'+delta gleq 0,quaddelta>0,$$ but only asking that $g$ vanishes exponentially fast.","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43926281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-09DOI: 10.1512/iumj.2022.71.9589
A. Alarcón
We prove that the open unit ball Bn of C n (n ≥ 2) admits a nonsingular holomorphic foliation F by closed complex hypersurfaces such that both the union of the complete leaves of F and the union of the incomplete leaves of F are dense subsets of Bn. In particular, every leaf of F is both a limit of complete leaves of F and a limit of incomplete leaves of F . This gives the first example of a holomorphic foliation of Bn by connected closed complex hypersurfaces having a complete leaf that is a limit of incomplete ones. We obtain an analogous result for foliations by complex submanifolds of arbitrary pure codimension q with 1 ≤ q < n.
{"title":"Wild holomorphic foliations of the ball","authors":"A. Alarcón","doi":"10.1512/iumj.2022.71.9589","DOIUrl":"https://doi.org/10.1512/iumj.2022.71.9589","url":null,"abstract":"We prove that the open unit ball Bn of C n (n ≥ 2) admits a nonsingular holomorphic foliation F by closed complex hypersurfaces such that both the union of the complete leaves of F and the union of the incomplete leaves of F are dense subsets of Bn. In particular, every leaf of F is both a limit of complete leaves of F and a limit of incomplete leaves of F . This gives the first example of a holomorphic foliation of Bn by connected closed complex hypersurfaces having a complete leaf that is a limit of incomplete ones. We obtain an analogous result for foliations by complex submanifolds of arbitrary pure codimension q with 1 ≤ q < n.","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43755255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-05-05DOI: 10.1512/iumj.2023.72.9447
Lucas Hall, S. Kaliszewski, John Quigg, Dana P. Williams
Given a free and proper action of a groupoid on a Fell bundle (over another groupoid), we give an equivalence between the semidirect-product and the generalized-fixed-point Fell bundles, generalizing an earlier result where the action was by a group. As an application, we show that the Stabilization Theorem for Fell bundles over groupoids is essentially another form of crossed-product duality.
{"title":"Groupoid semidirect product Fell bundles II --- principal actions and stabilization","authors":"Lucas Hall, S. Kaliszewski, John Quigg, Dana P. Williams","doi":"10.1512/iumj.2023.72.9447","DOIUrl":"https://doi.org/10.1512/iumj.2023.72.9447","url":null,"abstract":"Given a free and proper action of a groupoid on a Fell bundle (over another groupoid), we give an equivalence between the semidirect-product and the generalized-fixed-point Fell bundles, generalizing an earlier result where the action was by a group. As an application, we show that the Stabilization Theorem for Fell bundles over groupoids is essentially another form of crossed-product duality.","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45245081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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