Pub Date : 2022-08-18DOI: 10.1142/s0219199722500614
C. O. Alves, Renan J. S. Isneri, P. Montecchiari
{"title":"Existence of Heteroclinic and Saddle type solutions for a class of quasilinear problems in whole ℝ2","authors":"C. O. Alves, Renan J. S. Isneri, P. Montecchiari","doi":"10.1142/s0219199722500614","DOIUrl":"https://doi.org/10.1142/s0219199722500614","url":null,"abstract":"","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42612341","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 : 2022-08-18DOI: 10.1142/s0219199722500602
Benniao Li, W. Long, Aliang Xia
{"title":"Multiple positive and sign-changing solutions for a class of kirchhoff equations","authors":"Benniao Li, W. Long, Aliang Xia","doi":"10.1142/s0219199722500602","DOIUrl":"https://doi.org/10.1142/s0219199722500602","url":null,"abstract":"","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44640992","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 : 2022-08-17DOI: 10.1142/s0219199723500359
Jordan Serres
We control the behavior of the Poincar{'e} constant along the Polchinski renormalization flow using a dynamic version of $Gamma$-calculus. We also treat the case of higher order eigenvalues. Our method generalizes a method introduced by B. Klartag and E. Putterman to analyze the evolution of log-concave distributions along the heat flow. Furthermore, we apply it to general $Phi$ 4-measures and discuss the interpretation in terms of transport maps.
{"title":"Behavior of the poincare constant along the polchinski renormalization flow","authors":"Jordan Serres","doi":"10.1142/s0219199723500359","DOIUrl":"https://doi.org/10.1142/s0219199723500359","url":null,"abstract":"We control the behavior of the Poincar{'e} constant along the Polchinski renormalization flow using a dynamic version of $Gamma$-calculus. We also treat the case of higher order eigenvalues. Our method generalizes a method introduced by B. Klartag and E. Putterman to analyze the evolution of log-concave distributions along the heat flow. Furthermore, we apply it to general $Phi$ 4-measures and discuss the interpretation in terms of transport maps.","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45526630","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 : 2022-07-20DOI: 10.1142/s0219199722500444
J. Bona, F. Weissler
{"title":"Blowup and ILL-Posedness for the Complex, Periodic KDV Equation","authors":"J. Bona, F. Weissler","doi":"10.1142/s0219199722500444","DOIUrl":"https://doi.org/10.1142/s0219199722500444","url":null,"abstract":"","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44899448","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 : 2022-07-11DOI: 10.1142/s0219199723500372
L. Brasco, Mar'ia de Mar Gonz'alez, M. Ispizua
Motivated by the connection between the first eigenvalue of the Dirichlet-Laplacian and the torsional rigidity, the aim of this paper is to find a physically coherent and mathematically interesting new concept for boundary torsional rigidity, closely related to the Steklov eigenvalue. From a variational point of view, such a new object corresponds to the sharp constant for the trace embedding of $W^{1,2}(Omega)$ into $L^1(partialOmega)$. We obtain various equivalent variational formulations, present some properties of the state function and obtain some sharp geometric estimates, both for planar simply connected sets and for convex sets in any dimension.
{"title":"A steklov version of the torsional rigidity","authors":"L. Brasco, Mar'ia de Mar Gonz'alez, M. Ispizua","doi":"10.1142/s0219199723500372","DOIUrl":"https://doi.org/10.1142/s0219199723500372","url":null,"abstract":"Motivated by the connection between the first eigenvalue of the Dirichlet-Laplacian and the torsional rigidity, the aim of this paper is to find a physically coherent and mathematically interesting new concept for boundary torsional rigidity, closely related to the Steklov eigenvalue. From a variational point of view, such a new object corresponds to the sharp constant for the trace embedding of $W^{1,2}(Omega)$ into $L^1(partialOmega)$. We obtain various equivalent variational formulations, present some properties of the state function and obtain some sharp geometric estimates, both for planar simply connected sets and for convex sets in any dimension.","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43596438","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 : 2022-05-25DOI: 10.1142/S0219199722500754
F. Podestà, Alberto Raffero
. Starting from compact symmetric spaces of inner type, we provide infinite families of compact homogeneous spaces carrying invariant non-flat Bismut connections with vanishing Ricci tensor. These examples turn out to be generalized symmetric spaces of order 4 and (up to coverings) can be realized as minimal submanifolds of the Bismut flat model spaces, namely compact Lie groups. This construction generalizes the standard Cartan embedding of symmetric spaces.
{"title":"Infinite families of homogeneous bismut ricci flat manifolds","authors":"F. Podestà, Alberto Raffero","doi":"10.1142/S0219199722500754","DOIUrl":"https://doi.org/10.1142/S0219199722500754","url":null,"abstract":". Starting from compact symmetric spaces of inner type, we provide infinite families of compact homogeneous spaces carrying invariant non-flat Bismut connections with vanishing Ricci tensor. These examples turn out to be generalized symmetric spaces of order 4 and (up to coverings) can be realized as minimal submanifolds of the Bismut flat model spaces, namely compact Lie groups. This construction generalizes the standard Cartan embedding of symmetric spaces.","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64399644","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 : 2022-05-17DOI: 10.1142/S0219199722500821
Xiaoliang Li, Cong Wang
. We treat the exterior Dirichlet problem for a class of fully nonlinear elliptic equations of the form f ( λ ( D 2 u )) = g ( x ) , with prescribed asymptotic behavior at infinity. The equations of this type had been studied extensively by Caffarelli–Nirenberg–Spruck [8], Trudinger [35] and many others, and there had been significant discussions on the solv- ability of the classical Dirichlet problem via the continuity method, under the assumption that f is a concave function. In this paper, based on the Perron’s method, we establish an exterior existence and uniqueness result for viscosity solutions of the equations, by assuming f to satisfy certain structure condi- tions as in [8, 35] but without requiring the concavity of f . The equations in our setting may embrace the well-known Monge–Amp`ere equations, Hessian equations and Hessian quotient equations as special cases.
。我们处理了一类形式为f (λ (d2 u)) = g (x)的完全非线性椭圆方程的外部Dirichlet问题，该方程在无穷远处具有规定的渐近行为。Caffarelli-Nirenberg-Spruck [8]， Trudinger[8]等人对这类方程进行了广泛的研究，并在假设f为凹函数的情况下，对经典Dirichlet问题用连续性方法的可解性进行了有意义的讨论。本文基于Perron方法，假设f满足[8,35]中的某些结构条件，但不需要f的凹性，建立了方程黏度解的外部存在唯一性结果。我们设置的方程可以包括著名的Monge-Amp 'ere方程，Hessian方程和Hessian商方程作为特殊情况。
{"title":"On the exterior Dirichlet problem for Hessian type fully nonlinear elliptic equations","authors":"Xiaoliang Li, Cong Wang","doi":"10.1142/S0219199722500821","DOIUrl":"https://doi.org/10.1142/S0219199722500821","url":null,"abstract":". We treat the exterior Dirichlet problem for a class of fully nonlinear elliptic equations of the form f ( λ ( D 2 u )) = g ( x ) , with prescribed asymptotic behavior at infinity. The equations of this type had been studied extensively by Caffarelli–Nirenberg–Spruck [8], Trudinger [35] and many others, and there had been significant discussions on the solv- ability of the classical Dirichlet problem via the continuity method, under the assumption that f is a concave function. In this paper, based on the Perron’s method, we establish an exterior existence and uniqueness result for viscosity solutions of the equations, by assuming f to satisfy certain structure condi- tions as in [8, 35] but without requiring the concavity of f . The equations in our setting may embrace the well-known Monge–Amp`ere equations, Hessian equations and Hessian quotient equations as special cases.","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48193946","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 : 2022-05-05DOI: 10.1142/s0219199723500013
Huxiao Luo, B. Ruf, C. Tarsi
: We consider the semilinear elliptic equations where I α is a Riesz potential, p ∈ ( N + αN , N + α N − 2 ), N ≥ 3, and V is continuous periodic. We assume that 0 lies in the spectral gap ( a, b ) of − ∆ + V . We prove the existence of infinitely many geometrically distinct solutions in H 1 ( R N ) for each λ ∈ ( a, b ), which bifurcate from b if N + αN < p < 1 + 2+ αN . Moreover, b is the unique gap-bifurcation point (from zero) in [ a, b ]. When λ = a , we find infinitely many geometrically distinct solutions in H 2 loc ( R N ). Final remarks are given about the eventual occurrence of a bifurcation from infinity in λ = a . 35Q55, 47J35.
{"title":"Bifurcation into spectral gaps for strongly indefinite Choquard equations","authors":"Huxiao Luo, B. Ruf, C. Tarsi","doi":"10.1142/s0219199723500013","DOIUrl":"https://doi.org/10.1142/s0219199723500013","url":null,"abstract":": We consider the semilinear elliptic equations where I α is a Riesz potential, p ∈ ( N + αN , N + α N − 2 ), N ≥ 3, and V is continuous periodic. We assume that 0 lies in the spectral gap ( a, b ) of − ∆ + V . We prove the existence of infinitely many geometrically distinct solutions in H 1 ( R N ) for each λ ∈ ( a, b ), which bifurcate from b if N + αN < p < 1 + 2+ αN . Moreover, b is the unique gap-bifurcation point (from zero) in [ a, b ]. When λ = a , we find infinitely many geometrically distinct solutions in H 2 loc ( R N ). Final remarks are given about the eventual occurrence of a bifurcation from infinity in λ = a . 35Q55, 47J35.","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44658255","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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