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Preface for the special issue in honor of David Jerison 纪念大卫·杰伦的特刊序言
2区 数学
Advanced Nonlinear Studies Pub Date : 2023-01-01 DOI: 10.1515/ans-2023-0106
Guozhen Lu
{"title":"Preface for the special issue in honor of David Jerison","authors":"Guozhen Lu","doi":"10.1515/ans-2023-0106","DOIUrl":"https://doi.org/10.1515/ans-2023-0106","url":null,"abstract":"","PeriodicalId":7191,"journal":{"name":"Advanced Nonlinear Studies","volume":"155 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136008458","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}
引用次数: 0
On degenerate case of prescribed curvature measure problems 关于规定曲率测量问题的退化情况
IF 1.8 2区 数学
Advanced Nonlinear Studies Pub Date : 2023-01-01 DOI: 10.1515/ans-2022-0035
Guohuan Qiu, J. Suo
{"title":"On degenerate case of prescribed curvature measure problems","authors":"Guohuan Qiu, J. Suo","doi":"10.1515/ans-2022-0035","DOIUrl":"https://doi.org/10.1515/ans-2022-0035","url":null,"abstract":"Abstract In this article, we prove the C1,1 estimate for solutions of prescribed curvature measure problems when the prescribed function may touch zero somewhere.","PeriodicalId":7191,"journal":{"name":"Advanced Nonlinear Studies","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43168464","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}
引用次数: 0
Capillary Schwarz symmetrization in the half-space 半空间中的毛细Schwarz对称
IF 1.8 2区 数学
Advanced Nonlinear Studies Pub Date : 2023-01-01 DOI: 10.1515/ans-2022-0078
Zheng Lu, C. Xia, Xuwen Zhang
{"title":"Capillary Schwarz symmetrization in the half-space","authors":"Zheng Lu, C. Xia, Xuwen Zhang","doi":"10.1515/ans-2022-0078","DOIUrl":"https://doi.org/10.1515/ans-2022-0078","url":null,"abstract":"Abstract In this article, we introduce a notion of capillary Schwarz symmetrization in the half-space. It can be viewed as the counterpart of the classical Schwarz symmetrization in the framework of capillary problem in the half-space. A key ingredient is a special anisotropic gauge, which enables us to transform the capillary symmetrization to the convex symmetrization introduced in Alvino et al. https:/doi.org/10.1016/S0294-1449(97)80147-3.","PeriodicalId":7191,"journal":{"name":"Advanced Nonlinear Studies","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43292665","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}
引用次数: 2
The Neumann problem on the domain in 𝕊3 bounded by the Clifford torus 以Clifford环面为界的𝕊3上的Neumann问题
IF 1.8 2区 数学
Advanced Nonlinear Studies Pub Date : 2023-01-01 DOI: 10.1515/ans-2022-0072
Jeffrey S. Case, Eric Chen, Yi Wang, Paul Yang, Po-Lam Yung
{"title":"The Neumann problem on the domain in 𝕊3 bounded by the Clifford torus","authors":"Jeffrey S. Case, Eric Chen, Yi Wang, Paul Yang, Po-Lam Yung","doi":"10.1515/ans-2022-0072","DOIUrl":"https://doi.org/10.1515/ans-2022-0072","url":null,"abstract":"Abstract In this study, the solution of the Neumann problem associated with the CR Yamabe operator on a subset Ω Omega of the CR manifold S 3 {{mathbb{S}}}^{3} bounded by the Clifford torus Σ Sigma is discussed. The Yamabe-type problem of finding a contact form on Ω Omega which has zero Tanaka-Webster scalar curvature and for which Σ Sigma has a constant p p -mean curvature is also discussed.","PeriodicalId":7191,"journal":{"name":"Advanced Nonlinear Studies","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45988183","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}
引用次数: 0
Smooth approximation of twisted Kähler-Einstein metrics 扭曲Kähler-Einstein指标的平滑逼近
IF 1.8 2区 数学
Advanced Nonlinear Studies Pub Date : 2023-01-01 DOI: 10.1515/ans-2022-0032
Lize Jin, Feng Wang
{"title":"Smooth approximation of twisted Kähler-Einstein metrics","authors":"Lize Jin, Feng Wang","doi":"10.1515/ans-2022-0032","DOIUrl":"https://doi.org/10.1515/ans-2022-0032","url":null,"abstract":"Abstract In this article, we prove the existence of smooth approximations of twisted Kähler-Einstein metrics using the variational method.","PeriodicalId":7191,"journal":{"name":"Advanced Nonlinear Studies","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48831107","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}
引用次数: 0
A priori bounds, existence, and uniqueness of smooth solutions to an anisotropic Lp Minkowski problem for log-concave measure 对数凹测度的各向异性Lp Minkowski问题光滑解的先验界、存在性和唯一性
IF 1.8 2区 数学
Advanced Nonlinear Studies Pub Date : 2023-01-01 DOI: 10.1515/ans-2022-0068
Zhengmao Chen
{"title":"A priori bounds, existence, and uniqueness of smooth solutions to an anisotropic Lp Minkowski problem for log-concave measure","authors":"Zhengmao Chen","doi":"10.1515/ans-2022-0068","DOIUrl":"https://doi.org/10.1515/ans-2022-0068","url":null,"abstract":"Abstract In the present article, we prove the existence and uniqueness of smooth solutions to an anisotropic L p {L}_{p} Minkowski problem for the log-concave measure. Our proof of the existence is based on the well-known continuous method whose crucial factor is the a priori bounds of an auxiliary problem. The uniqueness is based on a maximum principle argument. It is worth mentioning that apart from the C 2 {C}^{2} bounds of solutions, the C 1 {C}^{1} bounds of solutions also need some efforts since the convexity of S S cannot be used directly, which is one of great difference between the classical and the anisotropic versions. Moreover, our result can be seen as an attempt to get new results on the geometric analysis of log-concave measure.","PeriodicalId":7191,"journal":{"name":"Advanced Nonlinear Studies","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42848564","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}
引用次数: 0
Improved fractional Trudinger-Moser inequalities on bounded intervals and the existence of their extremals 有界区间上改进的分数阶Trudinger-Moser不等式及其极值的存在性
IF 1.8 2区 数学
Advanced Nonlinear Studies Pub Date : 2023-01-01 DOI: 10.1515/ans-2022-0067
Lu Chen, Bohan Wang, Maochun Zhu
{"title":"Improved fractional Trudinger-Moser inequalities on bounded intervals and the existence of their extremals","authors":"Lu Chen, Bohan Wang, Maochun Zhu","doi":"10.1515/ans-2022-0067","DOIUrl":"https://doi.org/10.1515/ans-2022-0067","url":null,"abstract":"Abstract Let I I be a bounded interval of R {mathbb{R}} and λ 1 ( I ) {lambda }_{1}left(I) denote the first eigenvalue of the nonlocal operator ( − Δ ) 1 4 {(-Delta )}^{tfrac{1}{4}} with the Dirichlet boundary. We prove that for any 0 ⩽ α < λ 1 ( I ) 0leqslant alpha lt {lambda }_{1}(I) , there holds sup u ∈ W 0 1 2 , 2 ( I ) , ‖ ( − Δ ) 1 4 u ‖ 2 2 − α ∥ u ∥ 2 2 ≤ 1 ∫ I e π u 2 d x < + ∞ , mathop{sup }limits_{uin {W}_{0}^{frac{1}{2},2}(I),Vert {left(-Delta )}^{tfrac{1}{4}}u{Vert }_{2}^{2}-alpha {parallel uparallel }_{2}^{2}le 1}mathop{int }limits_{I}{e}^{pi {u}^{2}}{rm{d}}xlt +infty , and the supremum can be attained. The method is based on concentration-compactness principle for fractional Trudinger-Moser inequality, blow-up analysis for fractional elliptic equation with the critical exponential growth and harmonic extensions.","PeriodicalId":7191,"journal":{"name":"Advanced Nonlinear Studies","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48122382","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}
引用次数: 3
Quasilinear problems with nonlinear boundary conditions in higher-dimensional thin domains with corrugated boundaries 具有波纹边界的高维薄域非线性边界条件的拟线性问题
IF 1.8 2区 数学
Advanced Nonlinear Studies Pub Date : 2023-01-01 DOI: 10.1515/ans-2023-0101
J. C. Nakasato, M. Pereira
{"title":"Quasilinear problems with nonlinear boundary conditions in higher-dimensional thin domains with corrugated boundaries","authors":"J. C. Nakasato, M. Pereira","doi":"10.1515/ans-2023-0101","DOIUrl":"https://doi.org/10.1515/ans-2023-0101","url":null,"abstract":"Abstract In this work, we analyze the asymptotic behavior of a class of quasilinear elliptic equations defined in oscillating ( N + 1 ) left(N+1) -dimensional thin domains (i.e., a family of bounded open sets from R N + 1 {{mathbb{R}}}^{N+1} , with corrugated bounder, which degenerates to an open bounded set in R N {{mathbb{R}}}^{N} ). We also allow monotone nonlinear boundary conditions on the rough border whose magnitude depends on the squeezing of the domain. According to the intensity of the roughness and a reaction coefficient term on the nonlinear boundary condition, we obtain different regimes establishing effective homogenized limits in N N -dimensional open bounded sets. In order to do that, we combine monotone operator analysis techniques and the unfolding method used to deal with asymptotic analysis and homogenization problems.","PeriodicalId":7191,"journal":{"name":"Advanced Nonlinear Studies","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41535882","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}
引用次数: 0
Convex hypersurfaces with prescribed Musielak-Orlicz-Gauss image measure 具有规定的Musielak-Orlicz-Gauss图像测度的凸超曲面
IF 1.8 2区 数学
Advanced Nonlinear Studies Pub Date : 2023-01-01 DOI: 10.1515/ans-2022-0033
Qi-Rui Li, Caihong Yi
{"title":"Convex hypersurfaces with prescribed Musielak-Orlicz-Gauss image measure","authors":"Qi-Rui Li, Caihong Yi","doi":"10.1515/ans-2022-0033","DOIUrl":"https://doi.org/10.1515/ans-2022-0033","url":null,"abstract":"Abstract In this article, we study the Musielak-Orlicz-Gauss image problem based on the Gauss curvature flow in Li et al. We deal with some cases in which there is no uniform estimate for the Gauss curvature flow. By the use of the topological method in Guang et al., a special initial condition is chosen such that the Gauss curvature flow converges to a solution of the Musielak-Orlicz-Gauss image problem.","PeriodicalId":7191,"journal":{"name":"Advanced Nonlinear Studies","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48708261","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}
引用次数: 0
On some dense sets in the space of dynamical systems 关于动力系统空间中的一些稠密集
IF 1.8 2区 数学
Advanced Nonlinear Studies Pub Date : 2023-01-01 DOI: 10.1515/ans-2022-0053
R. Pawlak, Justyna Poprawa
{"title":"On some dense sets in the space of dynamical systems","authors":"R. Pawlak, Justyna Poprawa","doi":"10.1515/ans-2022-0053","DOIUrl":"https://doi.org/10.1515/ans-2022-0053","url":null,"abstract":"Abstract The natural consequence of the existence of different kinds of chaos is the study of their mutual dependence and the relationship between these concepts and the entropy of systems. This observation also applies to the local approach to this issue. In this article, we will focus on this problem in the context of “points focusing chaos.” We aim to show their mutual independence by considering the sets of appropriate periodic dynamical systems in the space of discrete dynamical systems.","PeriodicalId":7191,"journal":{"name":"Advanced Nonlinear Studies","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43111517","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}
引用次数: 0
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