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Uniform stability of equilibria in the inviscid limit for the Navier-Stokes-Korteweg system Navier-Stokes-Korteweg系统无粘极限平衡点的一致稳定性
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-30 DOI: 10.1016/j.jfa.2025.111156
Xueke Pu , Xiuli Xu , Jingjun Zhang
{"title":"Uniform stability of equilibria in the inviscid limit for the Navier-Stokes-Korteweg system","authors":"Xueke Pu ,&nbsp;Xiuli Xu ,&nbsp;Jingjun Zhang","doi":"10.1016/j.jfa.2025.111156","DOIUrl":"10.1016/j.jfa.2025.111156","url":null,"abstract":"<div><div>This paper considers a stability result for the three-dimensional Navier-Stokes-Korteweg system uniformly in the inviscid limit. We obtain a unique global smooth solution close to the constant equilibria <span><math><mo>(</mo><mn>1</mn><mo>,</mo><mrow><mn>0</mn><mo>)</mo></mrow></math></span>, independent of the viscosity parameter <em>ε</em>, assuming that the potential part of the initial velocity is small independently of the viscosity parameter <em>ε</em> while the incompressible part of the initial velocity is small compared to <em>ε</em>. The proof is based on the parabolic energy estimates and dispersive properties involving the method of space time resonances.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 12","pages":"Article 111156"},"PeriodicalIF":1.6,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766852","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 noncommutative integral on spectrally truncated spectral triples, and a link with quantum ergodicity 谱截断谱三元组上的非交换积分，以及具有量子遍历性的链路
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-30 DOI: 10.1016/j.jfa.2025.111154
Eva-Maria Hekkelman, Edward A. McDonald
{"title":"A noncommutative integral on spectrally truncated spectral triples, and a link with quantum ergodicity","authors":"Eva-Maria Hekkelman,&nbsp;Edward A. McDonald","doi":"10.1016/j.jfa.2025.111154","DOIUrl":"10.1016/j.jfa.2025.111154","url":null,"abstract":"<div><div>We propose a simple approximation of the noncommutative integral in noncommutative geometry for the Connes–Van Suijlekom paradigm of spectrally truncated spectral triples. A close connection between this approximation and the field of quantum ergodicity and work by Widom in particular immediately provides a Szegő limit formula for noncommutative geometry. We then make a connection to the density of states. Finally, we propose a definition for the ergodicity of geodesic flow for compact spectral triples. This definition is known in quantum ergodicity as uniqueness of the vacuum state for <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-dynamical systems, and for spectral triples where local Weyl laws hold this implies that the Dirac operator of the spectral triple is quantum ergodic. This brings to light a close connection between quantum ergodicity and Connes' integral formula.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 12","pages":"Article 111154"},"PeriodicalIF":1.6,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144780556","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 the existence of extensions for manifold-valued Sobolev maps on perforated domains 穿孔域上流形值Sobolev映射扩展的存在性
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-23 DOI: 10.1016/j.jfa.2025.111142
Chiara Gavioli , Leon Happ , Valerio Pagliari
{"title":"On the existence of extensions for manifold-valued Sobolev maps on perforated domains","authors":"Chiara Gavioli ,&nbsp;Leon Happ ,&nbsp;Valerio Pagliari","doi":"10.1016/j.jfa.2025.111142","DOIUrl":"10.1016/j.jfa.2025.111142","url":null,"abstract":"<div><div>Motivated by manifold-constrained homogenization problems, we construct suitable extensions for Sobolev functions defined on a perforated domain and taking values in a compact, connected <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-manifold without boundary. The proof combines a by now classical extension result for the unconstrained case with a retraction argument that heavily relies on the topological properties of the manifold. With the ultimate goal of providing necessary conditions for the existence of extensions for Sobolev maps between manifolds, we additionally investigate the relationship between this problem and the surjectivity of the trace operator for such functions.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111142"},"PeriodicalIF":1.6,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144738067","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
Hölder regularity of solutions of the steady Boltzmann equation with soft potentials Hölder具有软势的稳定玻尔兹曼方程解的规律性
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-23 DOI: 10.1016/j.jfa.2025.111146
Kung-Chien Wu , Kuan-Hsiang Wang
{"title":"Hölder regularity of solutions of the steady Boltzmann equation with soft potentials","authors":"Kung-Chien Wu ,&nbsp;Kuan-Hsiang Wang","doi":"10.1016/j.jfa.2025.111146","DOIUrl":"10.1016/j.jfa.2025.111146","url":null,"abstract":"<div><div>We consider the Hölder regularity of solutions to the steady Boltzmann equation with in-flow boundary condition in bounded and strictly convex domains <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> for gases with cutoff soft potential <span><math><mo>(</mo><mo>−</mo><mn>3</mn><mo>&lt;</mo><mi>γ</mi><mo>&lt;</mo><mn>0</mn><mo>)</mo></math></span>. We prove that there is a unique solution with a bounded <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> norm in space and velocity. This solution is Hölder continuous, and its order depends not only on the regularity of the incoming boundary data, but also on the potential power <em>γ</em>. The result for modulated soft potential case <span><math><mo>−</mo><mn>2</mn><mo>&lt;</mo><mi>γ</mi><mo>&lt;</mo><mn>0</mn></math></span> is similar to hard potential case <span><math><mo>(</mo><mn>0</mn><mo>≤</mo><mi>γ</mi><mo>&lt;</mo><mn>1</mn><mo>)</mo></math></span> since we have <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> velocity regularity from collision part. However, we observe that for very soft potential case <span><math><mo>(</mo><mo>−</mo><mn>3</mn><mo>&lt;</mo><mi>γ</mi><mo>≤</mo><mo>−</mo><mn>2</mn><mo>)</mo></math></span>, the regularity in velocity obtained by the collision part is lower (Hölder only), but the boundary regularity still can transfer to solution (in both space and velocity) by transport and collision part under the restriction of <em>γ</em>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111146"},"PeriodicalIF":1.6,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724549","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 refined Lusin type theorem for gradients 梯度的一个改进的Lusin型定理
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-23 DOI: 10.1016/j.jfa.2025.111152
Luigi De Masi, Andrea Marchese
{"title":"A refined Lusin type theorem for gradients","authors":"Luigi De Masi,&nbsp;Andrea Marchese","doi":"10.1016/j.jfa.2025.111152","DOIUrl":"10.1016/j.jfa.2025.111152","url":null,"abstract":"<div><div>We prove a refined version of the celebrated Lusin type theorem for gradients by Alberti, stating that any Borel vector field <em>f</em> coincides with the gradient of a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> function <em>g</em>, outside a set <em>E</em> of arbitrarily small Lebesgue measure. We replace the Lebesgue measure with any Radon measure <em>μ</em>, and we obtain that the estimate on the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> norm of <em>Dg</em> does not depend on <span><math><mi>μ</mi><mo>(</mo><mi>E</mi><mo>)</mo></math></span>, if the value of <em>f</em> is <em>μ</em>-a.e. orthogonal to the decomposability bundle of <em>μ</em>. We observe that our result implies the 1-dimensional version of the flat chain conjecture by Ambrosio and Kirchheim on the equivalence between metric currents and flat chains with finite mass in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> and we state a suitable generalization for <em>k</em>-forms, which would imply the validity of the conjecture in full generality.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111152"},"PeriodicalIF":1.6,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144738526","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
Carleman estimates for higher step Grushin operators 高阶Grushin算子的Carleman估计
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-23 DOI: 10.1016/j.jfa.2025.111150
Hendrik De Bie , Pan Lian
{"title":"Carleman estimates for higher step Grushin operators","authors":"Hendrik De Bie ,&nbsp;Pan Lian","doi":"10.1016/j.jfa.2025.111150","DOIUrl":"10.1016/j.jfa.2025.111150","url":null,"abstract":"<div><div>The higher step Grushin operators <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span> are a family of sub-elliptic operators which degenerate on a sub-manifold of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>+</mo><mi>m</mi></mrow></msup></math></span>. This paper establishes Carleman-type inequalities for these operators. It is achieved by deriving a weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>−</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span> estimate for the Grushin-harmonic projector. The crucial ingredient in the proof is the addition formula for Gegenbauer polynomials due to T. Koornwinder and Y. Xu. As a consequence, we obtain the strong unique continuation property for the Schrödinger operators <span><math><mo>−</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>+</mo><mi>V</mi></math></span> at points of the degeneracy manifold, where <em>V</em> belongs to certain <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>loc</mi></mrow><mrow><mi>r</mi></mrow></msubsup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>+</mo><mi>m</mi></mrow></msup><mo>)</mo></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111150"},"PeriodicalIF":1.6,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144722808","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
Weighted cscK metrics (I): A priori estimates 加权cscK指标(I)：先验估计
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-23 DOI: 10.1016/j.jfa.2025.111148
Eleonora Di Nezza, Simon Jubert, Abdellah Lahdili
{"title":"Weighted cscK metrics (I): A priori estimates","authors":"Eleonora Di Nezza,&nbsp;Simon Jubert,&nbsp;Abdellah Lahdili","doi":"10.1016/j.jfa.2025.111148","DOIUrl":"10.1016/j.jfa.2025.111148","url":null,"abstract":"<div><div>Let <em>X</em> be a compact Kähler manifold. In this paper we study the existence of constant weighted scalar curvature Kähler (weighted cscK) metrics on <em>X</em>. More precisely, we establish a priori <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>k</mi></mrow></msup></math></span>-estimates (<span><math><mi>k</mi><mo>≥</mo><mn>0</mn></math></span>) for the Kähler potential associated with these metrics, thereby extending a result due to Chen and Cheng in the classical cscK setting.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111148"},"PeriodicalIF":1.7,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144714551","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
The Dirichlet problem for the prescribed curvature equations in Minkowski space 闵可夫斯基空间中曲率方程的Dirichlet问题
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-23 DOI: 10.1016/j.jfa.2025.111149
Bin Wang
{"title":"The Dirichlet problem for the prescribed curvature equations in Minkowski space","authors":"Bin Wang","doi":"10.1016/j.jfa.2025.111149","DOIUrl":"10.1016/j.jfa.2025.111149","url":null,"abstract":"<div><div>We study the Dirichlet problem for functions whose graphs are spacelike hypersurfaces with prescribed curvature in the Minkowski space and we obtain some new interior second order estimates for admissible solutions to the corresponding fully nonlinear elliptic partial differential equations.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111149"},"PeriodicalIF":1.6,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144722867","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
Random exponential sums and lattice points in regions 区域中的随机指数和和格点
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-23 DOI: 10.1016/j.jfa.2025.111145
Faruk Temur, Cihan Sahillioğulları
{"title":"Random exponential sums and lattice points in regions","authors":"Faruk Temur,&nbsp;Cihan Sahillioğulları","doi":"10.1016/j.jfa.2025.111145","DOIUrl":"10.1016/j.jfa.2025.111145","url":null,"abstract":"<div><div>In this article we study two fundamental problems on exponential sums via randomization of frequencies with stochastic processes. These are the Hardy-Littlewood majorant problem, and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msup><mo>(</mo><mi>T</mi><mo>)</mo><mo>,</mo><mspace></mspace><mi>n</mi><mo>∈</mo><mi>N</mi></math></span> norms of exponential sums, which can also be interpreted as solutions of diophantine equations or lattice points on surfaces. We establish connections to the well known problems on lattice points in regions such as the Dirichlet divisor problem.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111145"},"PeriodicalIF":1.6,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144722807","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
Regularity in diffusion models with gradient activation 梯度活化扩散模型的规律性
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-23 DOI: 10.1016/j.jfa.2025.111147
Damião J. Araújo , Aelson O. Sobral , Eduardo V. Teixeira
{"title":"Regularity in diffusion models with gradient activation","authors":"Damião J. Araújo ,&nbsp;Aelson O. Sobral ,&nbsp;Eduardo V. Teixeira","doi":"10.1016/j.jfa.2025.111147","DOIUrl":"10.1016/j.jfa.2025.111147","url":null,"abstract":"<div><div>We prove regularity estimates for solutions of highly degenerate fully nonlinear elliptic equations. These are free boundary models in which a nonlinear diffusion process drives the system only in the region where the gradient surpasses a given threshold. The model is mathematically framed through a new notion of viscosity solutions, where test functions with insufficiently large gradients are disregarded. Our main result concerns the existence of a universal modulus of continuity for <em>Du</em>, up to the free boundary. Gradient bounds with respect to the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> norm are proven to be uniform with respect to the degree of degeneracy. Several new ingredients are needed and further applications of the methods are discussed at the end of the paper.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111147"},"PeriodicalIF":1.6,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766808","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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