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Interfaces and Free Boundaries最新文献

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$C^{1,alpha}$-regularity for a class of degenerate/singular fully non-linear elliptic equations 一类退化/奇异全非线性椭圆方程的 $C^{1,alpha}$-regularity
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2024-01-22 DOI: 10.4171/ifb/496
Sumiya Baasandorj, Sun-Sig Byun, Ki-Ahm Lee, Se-Chan Lee
{"title":"$C^{1,alpha}$-regularity for a class of degenerate/singular fully non-linear elliptic equations","authors":"Sumiya Baasandorj, Sun-Sig Byun, Ki-Ahm Lee, Se-Chan Lee","doi":"10.4171/ifb/496","DOIUrl":"https://doi.org/10.4171/ifb/496","url":null,"abstract":"","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139606897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Quantitative convergence of the ``bulk'' free boundary in an oscillatory obstacle problem 振荡障碍问题中 "大块 "自由边界的定量收敛性
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2023-12-21 DOI: 10.4171/ifb/501
Farhan Abedin, William M. Feldman
{"title":"Quantitative convergence of the ``bulk'' free boundary in an oscillatory obstacle problem","authors":"Farhan Abedin, William M. Feldman","doi":"10.4171/ifb/501","DOIUrl":"https://doi.org/10.4171/ifb/501","url":null,"abstract":"","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138952610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 two-phase free boundary with a logarithmic term 带有对数项的两相自由边界
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2023-11-22 DOI: 10.4171/ifb/502
Morteza Fotouhi, Somayeh Khademloo
{"title":"A two-phase free boundary with a logarithmic term","authors":"Morteza Fotouhi, Somayeh Khademloo","doi":"10.4171/ifb/502","DOIUrl":"https://doi.org/10.4171/ifb/502","url":null,"abstract":"","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139248428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Embeddedness of liquid-vapour interfaces in stable equilibrium 稳定平衡中液-气界面的嵌入性
4区 数学
Interfaces and Free Boundaries Pub Date : 2023-10-19 DOI: 10.4171/ifb/490
Costante Bellettini
{"title":"Embeddedness of liquid-vapour interfaces in stable equilibrium","authors":"Costante Bellettini","doi":"10.4171/ifb/490","DOIUrl":"https://doi.org/10.4171/ifb/490","url":null,"abstract":"We consider a classical (capillary) model for a one-phase liquid in equilibrium. The liquid (e.g., water) is subject to a volume constraint, it does not mix with the surrounding vapour (e.g., air), it may come into contact with solid supports (e.g., a container), and it is subject to the action of an analytic potential field (e.g., gravity). The region occupied by the liquid is described as a set of locally finite perimeter (Caccioppoli set) in $R^3$; no a priori regularity assumption is made on its boundary. The (twofold) scope in this note is to propose a weakest possible set of mathematical assumptions that sensibly describe a condition of stable equilibrium for the liquid-vapour interface (the capillary surface), and to infer from those that this interface is a smoothly embedded analytic surface. (The liquid-solid-vapour junction, or free boundary, can be present but is not analysed here.) The result relies fundamentally on the recent varifold regularity theory developed by the author and Wickramasekera, and on the identification of a suitable formulation of the stability condition.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135666551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
Error estimate for classical solutions to the heat equation in a moving thin domain and its limit equation 运动薄域热方程及其极限方程经典解的误差估计
4区 数学
Interfaces and Free Boundaries Pub Date : 2023-10-13 DOI: 10.4171/ifb/499
Tatsu-Hiko Miura
{"title":"Error estimate for classical solutions to the heat equation in a moving thin domain and its limit equation","authors":"Tatsu-Hiko Miura","doi":"10.4171/ifb/499","DOIUrl":"https://doi.org/10.4171/ifb/499","url":null,"abstract":"We consider the Neumann-type problem of the heat equation in a moving thin domain around a given closed moving hypersurface. The main result of this paper is an error estimate in the sup-norm for classical solutions to the thin domain problem and a limit equation on the moving hypersurface which appears in the thin-film limit of the heat equation. To prove the error estimate, we show a uniform a priori estimate for a classical solution to the thin domain problem based on the maximum principle. Moreover, we construct a suitable approximate solution to the thin domain problem from a classical solution to the limit equation based on an asymptotic expansion of the thin domain problem and apply the uniform a priori estimate to the difference of the approximate solution and a classical solution to the thin domain problem.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135918853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 novel finite element approximation of anisotropic curve shortening flow 各向异性曲线缩短流的一种新的有限元逼近
4区 数学
Interfaces and Free Boundaries Pub Date : 2023-10-07 DOI: 10.4171/ifb/500
Klaus Deckelnick, Robert Nürnberg
{"title":"A novel finite element approximation of anisotropic curve shortening flow","authors":"Klaus Deckelnick, Robert Nürnberg","doi":"10.4171/ifb/500","DOIUrl":"https://doi.org/10.4171/ifb/500","url":null,"abstract":"We extend the DeTurck trick from the classical isotropic curve shortening flow to the anisotropic setting. Here, the anisotropic energy density is allowed to depend on space, which allows an interpretation in the context of Finsler metrics, giving rise to, for instance, geodesic curvature flow in Riemannian manifolds. Assuming that the density is strictly convex and smooth, we introduce a novel weak formulation for anisotropic curve shortening flow. We then derive an optimal $H^1$-error bound for a continuous-in-time semidiscrete finite element approximation that uses piecewise linear elements. In addition, we consider some fully practical fully discrete schemes and prove their unconditional stability. Finally, we present several numerical simulations, including some convergence experiments that confirm the derived error bound, as well as applications to crystalline curvature flow and geodesic curvature flow.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135252054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Classification of global solutions of a free boundary problem in the plane 平面上自由边界问题整体解的分类
4区 数学
Interfaces and Free Boundaries Pub Date : 2023-09-13 DOI: 10.4171/ifb/494
Serena Dipierro, Aram Karakhanyan, Enrico Valdinoci
{"title":"Classification of global solutions of a free boundary problem in the plane","authors":"Serena Dipierro, Aram Karakhanyan, Enrico Valdinoci","doi":"10.4171/ifb/494","DOIUrl":"https://doi.org/10.4171/ifb/494","url":null,"abstract":"We classify non-trivial, non-negative, positively homogeneous solutions of the equation $$ Delta u=gamma u^{gamma-1} $$ in the plane. The problem is motivated by the analysis of the classical Alt–Phillips free boundary problem, but considered here with negative exponents $gamma$. The proof relies on several bespoke results for ordinary differential equations.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135690247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Instantaneous convexity breaking for the quasi-static droplet model 准静态液滴模型的瞬时凸破缺
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2023-08-15 DOI: 10.4171/ifb/498
Albert Chau, B. Weinkove
{"title":"Instantaneous convexity breaking for the quasi-static droplet model","authors":"Albert Chau, B. Weinkove","doi":"10.4171/ifb/498","DOIUrl":"https://doi.org/10.4171/ifb/498","url":null,"abstract":"","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87993911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Fully nonlinear free transmission problems 全非线性自由传输问题
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2023-06-02 DOI: 10.4171/ifb/489
Edgard A. Pimentel, Makson S. Santos
{"title":"Fully nonlinear free transmission problems","authors":"Edgard A. Pimentel, Makson S. Santos","doi":"10.4171/ifb/489","DOIUrl":"https://doi.org/10.4171/ifb/489","url":null,"abstract":"","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79427418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Stability of self-similar solutions to geometric flows 几何流自相似解的稳定性
4区 数学
Interfaces and Free Boundaries Pub Date : 2023-05-30 DOI: 10.4171/ifb/488
Hengrong Du, Nung Kwan Yip
{"title":"Stability of self-similar solutions to geometric flows","authors":"Hengrong Du, Nung Kwan Yip","doi":"10.4171/ifb/488","DOIUrl":"https://doi.org/10.4171/ifb/488","url":null,"abstract":"We show that self-similar solutions for the mean curvature flow, surface diffusion, and Willmore flow of entire graphs are stable upon perturbations of initial data with small Lipschitz norm. Roughly speaking, the perturbed solutions are asymptotically self-similar as time tends to infinity. Our results are built upon the global analytic solutions constructed by Koch and Lamm in 2012, the compactness arguments adapted by Asai and Giga in 2014, and the spatial equi-decay properties on certain weighted function spaces. The proof for all of the above flows are achieved in a unified framework by utilizing the estimates of the linearized operator.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135643219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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