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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
Neumann problems for the Stokes equations in convex domains 凸域上Stokes方程的Neumann问题
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-23 DOI: 10.1016/j.jfa.2025.111151
Jun Geng , Zhongwei Shen
{"title":"Neumann problems for the Stokes equations in convex domains","authors":"Jun Geng ,&nbsp;Zhongwei Shen","doi":"10.1016/j.jfa.2025.111151","DOIUrl":"10.1016/j.jfa.2025.111151","url":null,"abstract":"<div><div>This paper studies the Neumann boundary value problems for the Stokes equations in a convex domain in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>. We obtain nontangential maximal function estimates in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> and <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>p</mi></mrow></msup></math></span> estimates for <em>p</em> in certain ranges depending on <em>d</em>. These ranges are larger than the known ranges for Lipschitz domains. The proof relies on a <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msup></math></span> estimate for the Stokes equations in convex domains.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111151"},"PeriodicalIF":1.7,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703260","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
Sobolev inequality and its applications to nonlinear PDE on noncommutative Euclidean spaces Sobolev不等式及其在非交换欧几里德空间上的非线性偏微分方程中的应用
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-22 DOI: 10.1016/j.jfa.2025.111143
Michael Ruzhansky , Serikbol Shaimardan , Kanat Tulenov
{"title":"Sobolev inequality and its applications to nonlinear PDE on noncommutative Euclidean spaces","authors":"Michael Ruzhansky ,&nbsp;Serikbol Shaimardan ,&nbsp;Kanat Tulenov","doi":"10.1016/j.jfa.2025.111143","DOIUrl":"10.1016/j.jfa.2025.111143","url":null,"abstract":"<div><div>In this work, we study the Sobolev inequality on noncommutative Euclidean spaces. As a simple consequence, we obtain the Gagliardo–Nirenberg type inequality and as its application we show global well-posedness of nonlinear PDEs in the noncommutative Euclidean space. Moreover, we show that the logarithmic Sobolev inequality is equivalent to the Nash inequality for possibly different constants in this noncommutative setting by completing the list in noncommutative Varopoulos's theorem in <span><span>[54]</span></span>. Finally, we present a direct application of the Nash inequality to compute the time decay for solutions of the heat equation in the noncommutative setting.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111143"},"PeriodicalIF":1.7,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703259","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 local bifurcation theorem for McKean-Vlasov diffusions McKean-Vlasov扩散的一个局部分岔定理
IF 1.6 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-22 DOI: 10.1016/j.jfa.2025.111144
Shao-Qin Zhang
{"title":"A local bifurcation theorem for McKean-Vlasov diffusions","authors":"Shao-Qin Zhang","doi":"10.1016/j.jfa.2025.111144","DOIUrl":"10.1016/j.jfa.2025.111144","url":null,"abstract":"<div><div>We establish an existence result of a solution to a class of probability measure-valued equations, whose solutions can be associated with stationary distributions of many McKean-Vlasov diffusions with gradient-type drifts. Coefficients of the probability measure-valued equation may be discontinuous in the weak topology and the total variation norm. Owing to that the bifurcation point of the probability measure-valued equation is relevant to the phase transition point of the associated McKean-Vlasov diffusion, we establish a local Krasnosel'skii bifurcation theorem. The regularized determinant for Hilbert-Schmidt operators is used to derive our criteria for the bifurcation point. Concrete examples, including the granular media equation and the Vlasov-Fokker-Planck equation with quadratic interaction, are given to illustrate our results.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111144"},"PeriodicalIF":1.6,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144722868","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
Critical prescribed Q-curvature flow on closed even-dimensional manifolds with sign-changing functions 具有变符号函数的闭偶维流形上的临界规定q曲率流
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-16 DOI: 10.1016/j.jfa.2025.111133
Leilei Cui , Changfeng Gui , Haicheng Yan , Wen Yang
{"title":"Critical prescribed Q-curvature flow on closed even-dimensional manifolds with sign-changing functions","authors":"Leilei Cui ,&nbsp;Changfeng Gui ,&nbsp;Haicheng Yan ,&nbsp;Wen Yang","doi":"10.1016/j.jfa.2025.111133","DOIUrl":"10.1016/j.jfa.2025.111133","url":null,"abstract":"<div><div>In this article, we consider the prescribed <em>Q</em>-curvature equation<span><span><span><math><mi>P</mi><mi>u</mi><mo>=</mo><mi>ρ</mi><mrow><mo>(</mo><mfrac><mrow><mi>h</mi><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn><mi>n</mi><mi>u</mi></mrow></msup></mrow><mrow><msub><mrow><mo>∫</mo></mrow><mrow><mi>M</mi></mrow></msub><mi>h</mi><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn><mi>n</mi><mi>u</mi></mrow></msup><mi>d</mi><mi>μ</mi></mrow></mfrac><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mo>|</mo><mi>M</mi><msub><mrow><mo>|</mo></mrow><mrow><msub><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msub></mrow></mfrac><mo>)</mo></mrow><mspace></mspace><mspace></mspace><mtext>in</mtext><mspace></mspace><mspace></mspace><mi>M</mi><mo>,</mo></math></span></span></span> where <span><math><mo>(</mo><mi>M</mi><mo>,</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></math></span> is a closed 2<em>n</em>-dimensional Riemannian manifold, <span><math><mi>P</mi></math></span> represents the GJMS operator, which is (weakly) positive with a kernel of constant functions. The function <em>h</em> is smooth and sign-changing, while <em>ρ</em> is a positive constant. In the critical case with <span><math><mi>ρ</mi><mo>=</mo><msup><mrow><mn>4</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>!</mo><msup><mrow><mi>π</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, we employ a negative gradient-like flow method to establish the existence of solutions to this prescribed <em>Q</em>-curvature equation. Our approach extends the work of Li-Xu <span><span>[46]</span></span>, which focused on dimension 2, to general even dimensions. This result can also be viewed as a counterpart to <span><span>[8]</span></span> in the case where <em>h</em> is a sign-changing function.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111133"},"PeriodicalIF":1.7,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144670289","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
Topological structure of the space of composition operators on the Hardy space of Dirichlet series Dirichlet级数Hardy空间上复合算子空间的拓扑结构
IF 1.7 2区 数学
Journal of Functional Analysis Pub Date : 2025-07-15 DOI: 10.1016/j.jfa.2025.111134
Frédéric Bayart , Maofa Wang , Xingxing Yao
{"title":"Topological structure of the space of composition operators on the Hardy space of Dirichlet series","authors":"Frédéric Bayart ,&nbsp;Maofa Wang ,&nbsp;Xingxing Yao","doi":"10.1016/j.jfa.2025.111134","DOIUrl":"10.1016/j.jfa.2025.111134","url":null,"abstract":"<div><div>The aim of this paper is to study when two composition operators on the Hilbert space of Dirichlet series with square summable coefficients belong to the same component or when their difference is compact. As a corollary we show that if a linear combination of composition operators with polynomial symbols of degree at most 2 is compact, then each composition operator is compact.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111134"},"PeriodicalIF":1.7,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144656711","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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