发布求助
文献互助 智能选刊 最新文献

Archive for Rational Mechanics and Analysis最新文献

筛选
英文 中文
A New Minimax Principle and Application to the p-Laplace Equation 一个新的极大极小原理及其在p-拉普拉斯方程中的应用
IF 2.4 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-05-31 DOI: 10.1007/s00205-026-02214-3
Xu-Jia Wang, Xinyue Zhang
{"title":"A New Minimax Principle and Application to the p-Laplace Equation","authors":"Xu-Jia Wang,&nbsp;Xinyue Zhang","doi":"10.1007/s00205-026-02214-3","DOIUrl":"10.1007/s00205-026-02214-3","url":null,"abstract":"<div><p>We introduce a new minimax principle to prove the existence of multi-peak solutions to the Neumann problem of the <i>p</i>-Laplace equation </p><div><div><span>$$ -varepsilon ^p Delta _p u = u^{q-1} - u^{p-1} text {in} Omega , $$</span></div></div><p>where <span>(Omega )</span> is a bounded domain in <span>(mathbb {R}^n)</span> with <span>(C^2)</span>-boundary, <span>(1&lt;p&lt;n)</span> and <span>(p&lt;q&lt; frac{np}{n-p})</span>. The minimax principle will be applied to the set of peak functions, which is a subset of the Sobolev space <span>(W^{1,p} (Omega ))</span>. The argument is based on a combination of variational methods, topological degree theory, and gradient flow.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148173454","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}
引用次数: 0
An Inverse Signorini Obstacle Problem 逆Signorini障碍问题
IF 2.4 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-05-26 DOI: 10.1007/s00205-026-02197-1
Maarten V. de Hoop, Matti Lassas, Jinpeng Lu, Lauri Oksanen, Ziyao Zhao
{"title":"An Inverse Signorini Obstacle Problem","authors":"Maarten V. de Hoop,&nbsp;Matti Lassas,&nbsp;Jinpeng Lu,&nbsp;Lauri Oksanen,&nbsp;Ziyao Zhao","doi":"10.1007/s00205-026-02197-1","DOIUrl":"10.1007/s00205-026-02197-1","url":null,"abstract":"<div><p>We study the inverse problem of determining a Signorini obstacle from boundary measurements for the isotropic elasticity system. We prove that the obstacle can be uniquely determined by a single measurement of displacement and normal stress for the Signorini problem on an open subset of the boundary up to a natural obstruction. In addition to considering the Signorini problem, we develop techniques that can be used to study inverse problems for general differential inequalities.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-026-02197-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148009751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic Stability of the Composite Wave of Rarefaction Wave and Contact Wave to Nonlinear Viscoelasticity Model with Non-convex Flux 稀疏波与接触波复合波对非凸粘弹性模型的渐近稳定性
IF 2.4 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-05-26 DOI: 10.1007/s00205-026-02203-6
Zhenhua Guo, Meichen Hou, Guiqin Qiu, Lingda Xu
{"title":"Asymptotic Stability of the Composite Wave of Rarefaction Wave and Contact Wave to Nonlinear Viscoelasticity Model with Non-convex Flux","authors":"Zhenhua Guo,&nbsp;Meichen Hou,&nbsp;Guiqin Qiu,&nbsp;Lingda Xu","doi":"10.1007/s00205-026-02203-6","DOIUrl":"10.1007/s00205-026-02203-6","url":null,"abstract":"<div><p>We study wave propagation in viscoelastic materials based on a system of viscous conservation laws derived from the viscoelastic dynamic system with fading memory. In this model, the stress is a non-convex function of the strain, in contrast to the Euler equations of gas dynamics, which possess a convex constitutive relation. The non-convex nature of the viscoelastic model permits composite wave patterns within the same characteristic family, which greatly complicates the analysis of wave behavior. To address this challenge, we establish a new weighted Poincaré-type inequality for the study of the nonlinear stability of such composite wave patterns.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148009749","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}
引用次数: 0
Convergence of Drift-Diffusion PDEs Arising as Wasserstein Gradient Flows of Convex Functions 由凸函数的Wasserstein梯度流引起的漂移扩散偏微分方程的收敛性
IF 2.4 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-05-24 DOI: 10.1007/s00205-026-02200-9
Lénaïc Chizat, Maria Colombo, Xavier Fernández-Real
{"title":"Convergence of Drift-Diffusion PDEs Arising as Wasserstein Gradient Flows of Convex Functions","authors":"Lénaïc Chizat,&nbsp;Maria Colombo,&nbsp;Xavier Fernández-Real","doi":"10.1007/s00205-026-02200-9","DOIUrl":"10.1007/s00205-026-02200-9","url":null,"abstract":"<div><p>We study the quantitative convergence of drift-diffusion PDEs that arise as Wasserstein gradient flows of linearly convex functions over the space of probability measures on <span>(mathbb {R}^d)</span>. In this setting, the objective is in general not <i>displacement</i> convex, so it is not clear <i>a priori</i> whether global convergence even holds. Still, our analysis reveals that diffusion allows a favorable interaction between Wasserstein geometry and linear convexity, leading to a general quantitative convergence theory, analogous to that of gradient flows in convex settings in the Euclidean space. More specifically, we prove that if the objective is convex and suitably coercive, the suboptimality gap decreases at a rate <i>O</i>(1/<i>t</i>). This improves to a rate faster than any polynomial—or even exponential in compact settings—when the objective is strongly convex relative to the entropy. Our results extend the range of mean-field Langevin dynamics that enjoy quantitative convergence guarantees, and enable new applications to optimization over the space of probability measures. To illustrate this, we show quantitative convergence results for the minimization of entropy-regularized nonconvex problems, we propose and study an <i>approximate Fisher Information</i> regularization covered by our setting, and we apply our results to an estimator for trajectory inference which involves the minimization of the relative entropy with respect to the Wiener measure in path space.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148009714","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}
引用次数: 0
Unique Continuation for Area Minimizing Currents 面积最小电流的独特延续
IF 2.4 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-05-24 DOI: 10.1007/s00205-026-02190-8
Camillo Brena, Stefano Decio
{"title":"Unique Continuation for Area Minimizing Currents","authors":"Camillo Brena,&nbsp;Stefano Decio","doi":"10.1007/s00205-026-02190-8","DOIUrl":"10.1007/s00205-026-02190-8","url":null,"abstract":"<div><p>The main goal of this work is to prove an instance of the unique continuation principle for area minimizing integral currents. More precisely, we consider an <i>m</i>-dimensional area minimizing integral current and an <i>m</i>-dimensional minimal surface, both contained in <span>({mathbb {R}}^{n+m})</span> with <span>(nge 1)</span>. We show that if, in an integral sense, the current has an infinite order of contact with the minimal surface at a point, then the current and the minimal surface coincide in a neighbourhood of that point.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148009715","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}
引用次数: 0
Unbounded Yudovich Solutions of the Euler Equations 欧拉方程的无界Yudovich解
IF 2.4 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-05-23 DOI: 10.1007/s00205-026-02193-5
Dimitri Cobb, Herbert Koch
{"title":"Unbounded Yudovich Solutions of the Euler Equations","authors":"Dimitri Cobb,&nbsp;Herbert Koch","doi":"10.1007/s00205-026-02193-5","DOIUrl":"10.1007/s00205-026-02193-5","url":null,"abstract":"<div><p>In this article, we will study unbounded solutions of the 2D incompressible Euler equations. One of the motivating factors for this is that the usual functional framework for the Euler equations (for example based on finite energy conditions, such as <span>(L^2)</span>) does not respect some of the symmetries of the problem, such as Galileo invariance. Our main result, global existence and uniqueness of solutions for initial data with square-root growth <span>(O(|x|^{frac{1}{2} - varepsilon }))</span> and bounded vorticity, is based on two key ingredients. First, an integral decomposition of the pressure, and secondly examining local energy balance leading to solution estimates in local Morrey type spaces. We also prove continuity of the initial data to solution map by a substantial adaptation of Yudovich’s uniqueness argument.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-026-02193-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148009662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global Results for Weakly Dispersive KP-II Equations on the Cylinder 圆柱上弱色散KP-II方程的全局结果
IF 2.4 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-05-23 DOI: 10.1007/s00205-026-02208-1
Sebastian Herr, Robert Schippa, Nikolay Tzvetkov
{"title":"Global Results for Weakly Dispersive KP-II Equations on the Cylinder","authors":"Sebastian Herr,&nbsp;Robert Schippa,&nbsp;Nikolay Tzvetkov","doi":"10.1007/s00205-026-02208-1","DOIUrl":"10.1007/s00205-026-02208-1","url":null,"abstract":"<div><p>We consider the dispersion-generalized KP-II equation on a partially periodic domain in the weakly dispersive regime. We use Fourier decoupling techniques to derive essentially sharp Strichartz estimates. With these in hand, we show that global well-posedness of the quasilinear Cauchy problem in <span>(L^2(mathbb {R}times mathbb {T}))</span>. Finally, we prove a long-time decay property of solutions with small mass by using the Kato smoothing effect in the fractional case.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-026-02208-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148009663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Role of the Viscosity Parameters in the Large Time Asymptotics of Two Dimensional Micropolar Flows 粘度参数在二维微极流大时间渐近中的作用
IF 2.4 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-05-21 DOI: 10.1007/s00205-026-02192-6
L. Brandolese, A. V. Busuioc, D. Iftimie, C. F. Perusato
{"title":"On the Role of the Viscosity Parameters in the Large Time Asymptotics of Two Dimensional Micropolar Flows","authors":"L. Brandolese,&nbsp;A. V. Busuioc,&nbsp;D. Iftimie,&nbsp;C. F. Perusato","doi":"10.1007/s00205-026-02192-6","DOIUrl":"10.1007/s00205-026-02192-6","url":null,"abstract":"<div><p>We investigate the role of the four viscosity parameters in fluids where the particles possess a microstructure (micropolar flows) and are allowed to rotate in a two-dimensional setting. We first establish the existence of global finite energy solutions, satisfying the classical energy equality, for arbitrary initial data in <span>(L^2)</span>, in the case of a spin viscosity <span>(gamma ge 0)</span>, and we construct the asymptotic profiles of the solution as <span>(trightarrow +infty )</span>. We deduce the remarkable fact that the large time behavior only depends on the kinematic viscosity <span>(mu )</span>, and not on the other parameters <span>(chi )</span> (vortex-viscosity), <span>(gamma )</span> (spin viscosity) and <span>(kappa )</span> (gyroviscosity) of the model. Our primary tool is a new enstrophy-like identity of independent interest, involving the difference between the fluid vorticity and the micro-angular velocity. Another consequence of our analysis is the identification of scenarios where the presence of micro-rotational effects significantly enhances dissipation, thereby slowing down the fluid motion at large times.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148009411","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}
引用次数: 0
From Wave-Functions to Single Boson Densities 从波函数到单玻色子密度
IF 2.4 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-05-21 DOI: 10.1007/s00205-026-02207-2
U. Bindini, L. De Pascale
{"title":"From Wave-Functions to Single Boson Densities","authors":"U. Bindini,&nbsp;L. De Pascale","doi":"10.1007/s00205-026-02207-2","DOIUrl":"10.1007/s00205-026-02207-2","url":null,"abstract":"<div><p>We investigate some of the properties of the mapping from wave-functions to single particle densities, partially answering an open question posed by E. H. Lieb in 1983.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-026-02207-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148009412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Half-Space Liouville Theorem for Anisotropic Minimal Graph with Free Boundary 具有自由边界的各向异性极小图的半空间Liouville定理
IF 2.4 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-05-18 DOI: 10.1007/s00205-026-02196-2
Guofang Wang, Wei Wei, Chao Xia, Xuwen Zhang
{"title":"A Half-Space Liouville Theorem for Anisotropic Minimal Graph with Free Boundary","authors":"Guofang Wang,&nbsp;Wei Wei,&nbsp;Chao Xia,&nbsp;Xuwen Zhang","doi":"10.1007/s00205-026-02196-2","DOIUrl":"10.1007/s00205-026-02196-2","url":null,"abstract":"<div><p>In this paper we prove the following Liouville-type theorem: any anisotropic minimal graph with free boundary in the half-space must be flat, provided that the graph function has at most one-sided linear growth. This extends the classical results of Bombieri–De Giorgi–Miranda (Arch Rational Mech Anal 32:255–267, 1969) and Simon (Indiana Univ Math J 25:821–855, 1976) to an appropriate free boundary setting.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-026-02196-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148008638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信
小红书