Journal de Mathematiques Pures et Appliquees最新文献

{"title":"Harmonic analysis in Dunkl settings","authors":"The Anh Bui","doi":"10.1016/j.matpur.2025.103725","DOIUrl":"10.1016/j.matpur.2025.103725","url":null,"abstract":"<div><div>Let <em>L</em> be the Dunkl Laplacian on the Euclidean space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> associated with a normalized root <em>R</em> and a multiplicity function <span><math><mi>k</mi><mo>(</mo><mi>ν</mi><mo>)</mo><mo>≥</mo><mn>0</mn><mo>,</mo><mi>ν</mi><mo>∈</mo><mi>R</mi></math></span>. In this paper, we first prove that the Besov and Triebel-Lizorkin spaces associated with the Dunkl Laplacian <em>L</em> are identical to the Besov and Triebel-Lizorkin spaces defined in the space of homogeneous type <span><math><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo><mo>‖</mo><mo>⋅</mo><mo>‖</mo><mo>,</mo><mi>d</mi><mi>w</mi><mo>)</mo></math></span>, where <span><math><mi>d</mi><mi>w</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msub><mrow><mo>∏</mo></mrow><mrow><mi>ν</mi><mo>∈</mo><mi>R</mi></mrow></msub><msup><mrow><mo>〈</mo><mi>ν</mi><mo>,</mo><mi>x</mi><mo>〉</mo></mrow><mrow><mi>k</mi><mo>(</mo><mi>ν</mi><mo>)</mo></mrow></msup><mi>d</mi><mi>x</mi></math></span>. Next, consider the Dunkl transform denoted by <span><math><mi>F</mi></math></span>. We introduce the multiplier operator <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span>, defined as <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>m</mi></mrow></msub><mi>f</mi><mo>=</mo><msup><mrow><mi>F</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>m</mi><mi>F</mi><mi>f</mi><mo>)</mo></math></span>, where <em>m</em> is a bounded function defined on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>. Our second aim is to prove multiplier theorems, including the Hörmander multiplier theorem, for <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> on the Besov and Tribel-Lizorkin spaces in the space of homogeneous type <span><math><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo><mo>‖</mo><mo>⋅</mo><mo>‖</mo><mo>,</mo><mi>d</mi><mi>w</mi><mo>)</mo></math></span>. Importantly, our findings present novel results, even in the specific case of the Hardy spaces.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"199 ","pages":"Article 103725"},"PeriodicalIF":2.1,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143917987","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}

{"title":"Long time behaviour of the solution of Maxwell's equations in dissipative generalized Lorentz materials (II) A modal approach","authors":"Maxence Cassier ,&nbsp;Patrick Joly ,&nbsp;Luis Alejandro Rosas Martínez","doi":"10.1016/j.matpur.2025.103720","DOIUrl":"10.1016/j.matpur.2025.103720","url":null,"abstract":"<div><div>This work concerns the analysis of electromagnetic dispersive media modelled by generalized Lorentz models. More precisely, this paper is the second of two articles dedicated to the long time behaviour of solutions of Maxwell's equations in dissipative Lorentz media, via the decay rate of the electromagnetic energy for the corresponding Cauchy problem. In opposition to the frequency dependent Lyapunov functions approach used in <span><span>[4]</span></span>, we develop a method based on the spectral analysis of the underlying non selfadjoint operator of the model. Although more involved, this approach is closer to physics, as it uses the dispersion relation of the model, and has the advantage to provide more precise and more optimal results, leading to distinguish the notion of weak and strong dissipation.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"201 ","pages":"Article 103720"},"PeriodicalIF":2.1,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144117002","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}

{"title":"Almost-everywhere uniqueness of Lagrangian trajectories for 3D Navier–Stokes revisited","authors":"Lucio Galeati","doi":"10.1016/j.matpur.2025.103723","DOIUrl":"10.1016/j.matpur.2025.103723","url":null,"abstract":"<div><div>We show that, for any Leray solution <em>u</em> to the 3D Navier–Stokes equations with <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, the associated deterministic and stochastic Lagrangian trajectories are unique for <em>Lebesgue a.e.</em> initial condition. Additionally, if <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></math></span>, then pathwise uniqueness is established for the stochastic Lagrangian trajectories starting from <em>every</em> initial condition. The result sharpens and extends the original one by Robinson and Sadowski <span><span>[1]</span></span> and is based on rather different techniques. A key role is played by a newly established asymmetric Lusin–Lipschitz property of Leray solutions <em>u</em>, in the framework of (random) Regular Lagrangian flows.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"200 ","pages":"Article 103723"},"PeriodicalIF":2.1,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143907562","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}

{"title":"Sticky-reflecting diffusion as a Wasserstein gradient flow","authors":"Jean-Baptiste Casteras ,&nbsp;Léonard Monsaingeon ,&nbsp;Filippo Santambrogio","doi":"10.1016/j.matpur.2025.103721","DOIUrl":"10.1016/j.matpur.2025.103721","url":null,"abstract":"<div><div>In this paper we identify the Fokker-Planck equation for (reflected) Sticky Brownian Motion as a Wasserstein gradient flow in the space of probability measures. The driving functional is the relative entropy with respect to a non-standard reference measure, the sum of an absolutely continuous interior part plus a singular part supported on the boundary. Taking the small time-step limit in a minimizing movement (JKO scheme) we prove existence of weak solutions for the coupled system of PDEs satisfying in addition an Energy Dissipation Inequality.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"199 ","pages":"Article 103721"},"PeriodicalIF":2.1,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143906987","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}

{"title":"An explicit Euler method for Sobolev vector fields with applications to the continuity equation on non Cartesian grids","authors":"Tommaso Cortopassi","doi":"10.1016/j.matpur.2025.103722","DOIUrl":"10.1016/j.matpur.2025.103722","url":null,"abstract":"<div><div>We prove a novel stability estimate in <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>t</mi></mrow><mrow><mo>∞</mo></mrow></msubsup><mo>(</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>x</mi></mrow><mrow><mi>p</mi></mrow></msubsup><mo>)</mo></math></span> between the regular Lagrangian flow of a Sobolev vector field and a piecewise affine approximation of such flow. This approximation of the flow is obtained by a (sort of) explicit Euler method, and it is the crucial tool to prove approximation results for the solution of the continuity equation by using the representation of the solution as the push-forward via the regular Lagrangian flow of the initial datum. We approximate the solution in two ways, using different approximations for both the flow and the initial datum. In the first case we give an estimate, which however holds only in probability, of the Wasserstein distance between the solution of the continuity equation and a discrete approximation of such solution. The approximate solution is defined as the push-forward of weighted Dirac deltas (whose centers are chosen in a probabilistic way). In the second case we give a deterministic estimate of the Wasserstein distance using a slightly different approximation of the regular Lagrangian flow and requiring more regularity on the velocity field <em>u</em> than in the previous case. An advantage of both approximations is that they provide an algorithm which is easily parallelizable and does not rely on any particular structure of the mesh with which we discretize (only in space) the domain. We also compare our estimates to similar ones previously obtained in <span><span>[27]</span></span>, and we show how under certain hypotheses our method provides better convergence rates.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"199 ","pages":"Article 103722"},"PeriodicalIF":2.1,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143906988","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}

{"title":"Viscosity driven instability of shear flows without boundaries","authors":"Hui Li ,&nbsp;Weiren Zhao","doi":"10.1016/j.matpur.2025.103724","DOIUrl":"10.1016/j.matpur.2025.103724","url":null,"abstract":"<div><div>In this paper, we study the instability effect of viscous dissipation in a domain without boundaries. We construct a shear flow that is initially spectrally stable but evolves into a spectrally unstable state under the influence of viscous dissipation. To the best of our knowledge, this is the first result of viscosity driven instability that is not caused by boundaries.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"200 ","pages":"Article 103724"},"PeriodicalIF":2.1,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895009","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}

{"title":"Properties of periodic Dirac–Fock functional and minimizers","authors":"Isabelle Catto ,&nbsp;Long Meng","doi":"10.1016/j.matpur.2025.103719","DOIUrl":"10.1016/j.matpur.2025.103719","url":null,"abstract":"<div><div>Existence of minimizers for the Dirac–Fock model for crystals was recently proved by Paturel and Séré and the authors <span><span>[9]</span></span>. In this paper, inspired by Ghimenti and Lewin's result <span><span>[13]</span></span> for the periodic Hartree–Fock model, we prove that the Fermi level of any periodic Dirac–Fock minimizer is either empty or totally filled when <span><math><mfrac><mrow><mi>α</mi></mrow><mrow><mi>c</mi></mrow></mfrac><mo>≤</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>cri</mi></mrow></msub></math></span> and <span><math><mi>α</mi><mo>&gt;</mo><mn>0</mn></math></span>. Here <em>c</em> is the speed of light, <em>α</em> is the fine structure constant, and <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>cri</mi></mrow></msub></math></span> is a constant only depending on the number of electrons and on the charge of nuclei per cell. More importantly, we provide an explicit upper bound for <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>cri</mi></mrow></msub></math></span>.</div><div>Our result implies that any minimizer of the periodic Dirac–Fock model is a projector when <span><math><mfrac><mrow><mi>α</mi></mrow><mrow><mi>c</mi></mrow></mfrac><mo>≤</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>cri</mi></mrow></msub></math></span> and <span><math><mi>α</mi><mo>&gt;</mo><mn>0</mn></math></span>. In particular, the non-relativistic regime (i.e., <span><math><mi>c</mi><mo>≫</mo><mn>1</mn></math></span>) and the weak coupling regime (i.e., <span><math><mn>0</mn><mo>&lt;</mo><mi>α</mi><mo>≪</mo><mn>1</mn></math></span>) are covered.</div><div>The proof is based on a delicate study of a second-order expansion of the periodic Dirac–Fock functional composed with a retraction that was introduced by Séré in <span><span>[24]</span></span> for atoms and molecules and later extended to the case of crystals in <span><span>[9]</span></span>.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"201 ","pages":"Article 103719"},"PeriodicalIF":2.1,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144067943","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}

{"title":"Critical mass phenomena and blow-up behaviors of ground states in stationary second order mean-field games systems with decreasing cost","authors":"Marco Cirant ,&nbsp;Fanze Kong ,&nbsp;Juncheng Wei ,&nbsp;Xiaoyu Zeng","doi":"10.1016/j.matpur.2025.103687","DOIUrl":"10.1016/j.matpur.2025.103687","url":null,"abstract":"<div><div>This paper is devoted to the study of Mean-field Games (MFG) systems in the mass-critical exponent case. We first derive the optimal Gagliardo-Nirenberg type inequality associated with the potential-free MFG system. Then, under some mild assumptions on the potential function, we show that there exists a critical mass <span><math><msup><mrow><mi>M</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> such that the MFG system admits a least-energy solution if and only if the total mass of population density <em>M</em> satisfies <span><math><mi>M</mi><mo>&lt;</mo><msup><mrow><mi>M</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>. Moreover, the blow-up behavior of energy minimizers is characterized as <span><math><mi>M</mi><mo>↗</mo><msup><mrow><mi>M</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>. In particular, by considering the precise asymptotic expansions of the potential, we establish the refined blow-up behavior of ground states as <span><math><mi>M</mi><mo>↗</mo><msup><mrow><mi>M</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>. While studying the existence of least-energy solutions, we establish new local <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>2</mn><mo>,</mo><mi>p</mi></mrow></msup></math></span> estimates for solutions to Hamilton-Jacobi equations with superlinear gradient terms.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"198 ","pages":"Article 103687"},"PeriodicalIF":2.1,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143534554","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}

{"title":"Reconstruction along a geodesic from sphere data in Finsler geometry and anisotropic elasticity","authors":"Maarten V. de Hoop ,&nbsp;Joonas Ilmavirta ,&nbsp;Matti Lassas","doi":"10.1016/j.matpur.2025.103688","DOIUrl":"10.1016/j.matpur.2025.103688","url":null,"abstract":"<div><div>Dix formulated the inverse problem of recovering an elastic body from the measurements of wave fronts of point sources. We geometrize this problem in the context of seismology, leading to the geometrical inverse problem of recovering a Finsler manifold from certain sphere data in a given open subset of the manifold. We solve this problem locally along any geodesic through the measurement set.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"196 ","pages":"Article 103688"},"PeriodicalIF":2.1,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143507519","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}

{"title":"Blowing up Chern-Ricci flat balanced metrics","authors":"Elia Fusi ,&nbsp;Federico Giusti","doi":"10.1016/j.matpur.2025.103691","DOIUrl":"10.1016/j.matpur.2025.103691","url":null,"abstract":"<div><div>Given a compact Chern-Ricci flat balanced orbifold, we show that its blow-up at a finite family of smooth points admits constant Chern scalar curvature balanced metrics, extending Arezzo-Pacard's construction to the balanced setting. Moreover, if the orbifold has isolated singularities and admits crepant resolutions, we show that they always carry Chern-Ricci flat balanced metrics, without any further hypothesis. Along the way, we study two Lichnerowicz-type operators originating from complex connections and investigate the relation between their kernel and holomorphic vector fields, with the aim of discussing the general constant Chern scalar curvature balanced case. Ultimately, we provide a variation of the main Theorem assuming the existence of a special <span><math><mo>(</mo><mi>n</mi><mo>−</mo><mn>2</mn><mo>,</mo><mi>n</mi><mo>−</mo><mn>2</mn><mo>)</mo></math></span>-form and we present several classes of examples in which all our results can be applied.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"197 ","pages":"Article 103691"},"PeriodicalIF":2.1,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509394","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}