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Sharp Quantitative Talenti Inequality in Particular Cases 特殊情况下的尖锐数量人才不平等
IF 2.4 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-04-03 DOI: 10.1007/s00205-026-02179-3
P. Acampora, J. Lamboley
{"title":"Sharp Quantitative Talenti Inequality in Particular Cases","authors":"P. Acampora,&nbsp;J. Lamboley","doi":"10.1007/s00205-026-02179-3","DOIUrl":"10.1007/s00205-026-02179-3","url":null,"abstract":"<div><p>In this paper, we focus on the famous Talenti’s symmetrization inequality, more precisely, its <span>(L^p)</span> corollary which asserts that the <span>(L^p)</span>-norm of the solution to <span>(-Delta v=f^sharp )</span> is higher than the <span>(L^p)</span>-norm of the solution to <span>(-Delta u=f)</span> (we are considering Dirichlet boundary conditions, and <span>(f^sharp )</span> denotes the Schwarz symmetrization of <span>(f:Omega rightarrow mathbb {R}_+)</span>). We focus on the particular case where functions <i>f</i> are defined on the unit ball, and are characteristic functions of a subset of this unit ball. We show in this case that stability occurs for the <span>(L^p)</span>-Talenti inequality with the sharp exponent 2.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147588615","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
Characterizing the Detailed Balance Property by Means of Measurements 用测量方法描述详细的平衡特性
IF 2.4 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-04-03 DOI: 10.1007/s00205-026-02183-7
Eugenia Franco, Bernhard Kepka, Juan J. L. Velázquez
{"title":"Characterizing the Detailed Balance Property by Means of Measurements","authors":"Eugenia Franco,&nbsp;Bernhard Kepka,&nbsp;Juan J. L. Velázquez","doi":"10.1007/s00205-026-02183-7","DOIUrl":"10.1007/s00205-026-02183-7","url":null,"abstract":"<div><p>In this paper we study how to determine if a linear biochemical network satisfies the detailed balance condition, without knowing the details of all the reactions taking place in the network. To this end, we use the formalism of response functions <span>(R_{ij} (t) )</span> that measure how the system reacts to the injection of the substance <i>j</i> at time <span>(t=0)</span>, by measuring the concentration of the substance <span>(i ne j)</span> for <span>(t &gt;0)</span>. In particular, we obtain a condition involving two reciprocal measurements (that is <span>(R_{ij}(t))</span>, <span>(R_{ji}(t))</span>) that is necessary, but not sufficient, for the detailed balance condition to hold in the network. Moreover, we prove that this necessary condition is also sufficient if a topological condition is satisfied by the graph associated to the network, as well as a stability property that guarantees that the chemical rates are not fine-tuned.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-026-02183-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147588616","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 Behavior of a Diffused Interface Volume-Preserving Mean Curvature Flow 一类保持体积的扩散界面平均曲率流的渐近性质
IF 2.4 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-03-31 DOI: 10.1007/s00205-026-02185-5
Matteo Bonforte, Francesco Maggi, Daniel Restrepo
{"title":"Asymptotic Behavior of a Diffused Interface Volume-Preserving Mean Curvature Flow","authors":"Matteo Bonforte,&nbsp;Francesco Maggi,&nbsp;Daniel Restrepo","doi":"10.1007/s00205-026-02185-5","DOIUrl":"10.1007/s00205-026-02185-5","url":null,"abstract":"<div><p>We consider a diffused interface version of the volume-preserving mean curvature flow in the Euclidean space, and prove, in every dimension and under natural assumptions on the initial datum, exponential convergence towards single “diffused balls”.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 2","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147607339","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
Existence of Constant Mean Curvature Disks in (mathbb {R}^3) with Capillary Boundary Condition 在毛细管边界条件下(mathbb {R}^3)中常平均曲率圆盘的存在性
IF 2.4 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-03-27 DOI: 10.1007/s00205-026-02165-9
Da Rong Cheng
{"title":"Existence of Constant Mean Curvature Disks in (mathbb {R}^3) with Capillary Boundary Condition","authors":"Da Rong Cheng","doi":"10.1007/s00205-026-02165-9","DOIUrl":"10.1007/s00205-026-02165-9","url":null,"abstract":"<div><p>We extend Struwe’s result (Acta Math. 160(1–2):19–64, 1988) on the existence of free boundary constant mean curvature disks to almost every prescribed boundary contact angle in <span>((0, pi ))</span>. Specifically, let <span>(Sigma )</span> be a surface in <span>(mathbb {R}^3)</span> diffeomorphic to the sphere, and let <span>(Sigma ')</span> be a convex surface enclosing <span>(Sigma )</span>. Given <span>(tau in (-1, 1))</span> and a constant <span>(H ge 0)</span> below the infimum of the mean curvature of <span>(Sigma ')</span>, we show that, for almost every <span>(r in (0, 1))</span>, in the region enclosed by <span>(Sigma ')</span>, there exists a branched immersed disk with constant mean curvature <i>rH</i> whose boundary meets <span>(Sigma )</span> at an angle with cosine value <span>(rtau )</span>. Moreover, the constant mean curvature disks we construct have index at most 1.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 2","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561477","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
A Stable-Compact Method for Qualitative Properties of Semilinear Elliptic Equations 半线性椭圆方程定性性质的稳定-紧化方法
IF 2.4 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-03-26 DOI: 10.1007/s00205-026-02168-6
Henri Berestycki, Cole Graham
{"title":"A Stable-Compact Method for Qualitative Properties of Semilinear Elliptic Equations","authors":"Henri Berestycki,&nbsp;Cole Graham","doi":"10.1007/s00205-026-02168-6","DOIUrl":"10.1007/s00205-026-02168-6","url":null,"abstract":"<div><p>We study the uniqueness of reaction-diffusion steady states in general domains with Dirichlet boundary data. Here we consider “positive” (monostable) reactions. We describe geometric conditions on the domain that ensure uniqueness and we provide complementary examples of nonuniqueness. Along the way, we formulate a number of open problems and conjectures. To derive our results, we develop a general framework, the <i>stable-compact method</i>, to study qualitative properties of nonlinear elliptic equations.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 2","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-026-02168-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560960","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 Continuation Criterion for the Landau Equation with Very Soft and Coulomb Potentials 具有极软和库仑势的朗道方程的延拓判据
IF 2.4 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-03-25 DOI: 10.1007/s00205-026-02182-8
Stanley Snelson, Caleb Solomon
{"title":"A Continuation Criterion for the Landau Equation with Very Soft and Coulomb Potentials","authors":"Stanley Snelson,&nbsp;Caleb Solomon","doi":"10.1007/s00205-026-02182-8","DOIUrl":"10.1007/s00205-026-02182-8","url":null,"abstract":"<div><p>We consider the spatially inhomogeneous Landau equation in the case of very soft and Coulomb potentials, <span>(gamma in [-3,-2])</span>. We show that solutions can be continued as long as the following three quantities remain finite, uniformly in <i>t</i> and <i>x</i>: (1) the mass density, (2) the velocity moment of order <i>s</i> for any small <span>(s&gt;0)</span>, and (3) the <span>(L^p_v)</span> norm for any <span>(p&gt;3/(5+gamma ))</span>. In particular, we do not require a bound on the energy density.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 2","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561835","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
Global Strong Solutions to the Compressible Navier–Stokes–Coriolis System for Large Data 大数据可压缩Navier-Stokes-Coriolis系统的全局强解
IF 2.4 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-03-24 DOI: 10.1007/s00205-026-02172-w
Mikihiro Fujii, Keiichi Watanabe
{"title":"Global Strong Solutions to the Compressible Navier–Stokes–Coriolis System for Large Data","authors":"Mikihiro Fujii,&nbsp;Keiichi Watanabe","doi":"10.1007/s00205-026-02172-w","DOIUrl":"10.1007/s00205-026-02172-w","url":null,"abstract":"<div><p>We consider the compressible Navier–Stokes system with the Coriolis force on the 3D whole space. In this model, the Coriolis force causes the linearized solution to behave like a 4th order dissipative semigroup <span>({ e^{-tDelta ^2} }_{t&gt;0})</span> with slower time decay rates than the heat kernel, which creates difficulties in nonlinear estimates in the low-frequency part and prevents us from constructing the global strong solutions by following the classical method. On account of this circumstance, the existence of unique global strong solutions has been open even in the classical Matsumura–Nishida framework. In this paper, we overcome the aforementioned difficulties and succeed in constructing a unique global strong solution in the framework of the scaling critical Besov space. Furthermore, our result also shows that the global solution is constructed for <i>large</i> initial data provided that the speed of the rotation is high and the Mach number is low enough by focusing on the dispersive effect due to the mixture of the Coriolis force and acoustic wave.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 2","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560918","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
The Long Way of a Viscous Vortex Dipole 粘性涡旋偶极子的漫漫长路
IF 2.4 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-03-22 DOI: 10.1007/s00205-026-02169-5
Michele Dolce, Thierry Gallay
{"title":"The Long Way of a Viscous Vortex Dipole","authors":"Michele Dolce,&nbsp;Thierry Gallay","doi":"10.1007/s00205-026-02169-5","DOIUrl":"10.1007/s00205-026-02169-5","url":null,"abstract":"<div><p>We consider the evolution of a viscous vortex dipole in <span>(mathbb {R}^2)</span> originating from a pair of point vortices with opposite circulations. At high Reynolds number <span>(textrm{Re}gg 1)</span>, the dipole can travel a very long way, compared to the distance between the vortex centers, before being slowed down and eventually destroyed by diffusion. In this regime we construct an accurate approximation of the solution in the form of a two-parameter asymptotic expansion involving the aspect ratio of the dipole and the inverse Reynolds number. We then show that the exact solution of the Navier–Stokes equations remains close to the approximation on a time interval of length <span>(mathcal {O}(textrm{Re}^sigma ))</span>, where <span>(sigma &lt; 1)</span> is arbitrary. This improves upon previous results which were essentially restricted to <span>(sigma = 0)</span>. As an application, we provide a rigorous justification of an existing formula which gives the leading order correction to the translation speed of the dipole due to finite size effects.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 2","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560791","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
A Free Boundary Monge–Ampère Equation and Applications to Complete Calabi–Yau Metrics 自由边界monge - ampantere方程及其在完全Calabi-Yau度量中的应用
IF 2.4 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-03-19 DOI: 10.1007/s00205-026-02175-7
Tristan C. Collins, Freid Tong, Shing-Tung Yau
{"title":"A Free Boundary Monge–Ampère Equation and Applications to Complete Calabi–Yau Metrics","authors":"Tristan C. Collins,&nbsp;Freid Tong,&nbsp;Shing-Tung Yau","doi":"10.1007/s00205-026-02175-7","DOIUrl":"10.1007/s00205-026-02175-7","url":null,"abstract":"<div><p>Let <i>P</i> be a convex body containing the origin in its interior. We study a real Monge–Ampère equation with singularities along <span>(partial P)</span> which is Legendre dual to a certain free boundary Monge–Ampère equation. This is motivated by the existence problem for complete Calabi–Yau metrics on log Calabi–Yau pairs (<i>X</i>, <i>D</i>) with <i>D</i> an ample, simple normal crossings divisor. We prove the existence of solutions in <span>(C^{infty }(P)cap C^{1,alpha }(overline{P}))</span>, and establish the strict convexity of the free boundary. When <i>P</i> is a polytope, we obtain an asymptotic expansion for the solution near the interior of the codimension 1 faces of <span>(partial P)</span>.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 2","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560108","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
Correction to: Free Boundary Problem for a Gas Bubble in a Liquid, and Exponential Stability of the Manifold of Spherically Symmetric Equilibria 修正：液体中气泡的自由边界问题，以及球对称平衡流形的指数稳定性
IF 2.4 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2026-03-16 DOI: 10.1007/s00205-025-02158-0
Chen-Chih Lai, Michael I. Weinstein
{"title":"Correction to: Free Boundary Problem for a Gas Bubble in a Liquid, and Exponential Stability of the Manifold of Spherically Symmetric Equilibria","authors":"Chen-Chih Lai,&nbsp;Michael I. Weinstein","doi":"10.1007/s00205-025-02158-0","DOIUrl":"10.1007/s00205-025-02158-0","url":null,"abstract":"","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"250 2","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147559568","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
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