Nonlinear Analysis-Theory Methods & Applications最新文献_第7页

Regularity and symmetry results for the vectorial p-Laplacian 矢量 p 拉普拉卡方的正则性和对称性结果

IF 1.3 2区数学

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-11-15 DOI: 10.1016/j.na.2024.113700

Luigi Montoro, Luigi Muglia, Berardino Sciunzi, Domenico Vuono

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Sobolev spaces for singular perturbation of 2D Laplace operator 二维拉普拉斯算子奇异扰动的索波列夫空间

IF 1.3 2区数学

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-11-15 DOI: 10.1016/j.na.2024.113710

Vladimir Georgiev , Mario Rastrelli

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Decay characterization of weak solutions for the MHD micropolar equations on R2 R2 上 MHD 弱解的衰减特征

IF 1.3 2区数学

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-11-15 DOI: 10.1016/j.na.2024.113701

Felipe W. Cruz, Mirelle M. Sousa

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Regularization estimates of the Landau–Coulomb diffusion 朗道-库仑扩散的正则化估计

IF 1.3 2区数学

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-11-13 DOI: 10.1016/j.na.2024.113695

Rene Cabrera , Maria Pia Gualdani , Nestor Guillen

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On the p-torsional rigidity of combinatorial graphs 论组合图的 p 扭转刚性

IF 1.3 2区数学

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-11-12 DOI: 10.1016/j.na.2024.113694

Patrizio Bifulco, Delio Mugnolo

{"title":"On the p-torsional rigidity of combinatorial graphs","authors":"Patrizio Bifulco, Delio Mugnolo","doi":"10.1016/j.na.2024.113694","DOIUrl":"10.1016/j.na.2024.113694","url":null,"abstract":"<div><div>We study the <span><math><mi>p</mi></math></span>-<em>torsion function</em> and the corresponding <span><math><mi>p</mi></math></span>-<em>torsional rigidity</em> associated with <span><math><mi>p</mi></math></span>-Laplacians and, more generally, <span><math><mi>p</mi></math></span>-Schrödinger operators, for <span><math><mrow><mn>1</mn><mo><</mo><mi>p</mi><mo><</mo><mi>∞</mi></mrow></math></span>, on possibly infinite combinatorial graphs. We present sufficient criteria for the existence of a summable <span><math><mi>p</mi></math></span>-torsion function and we derive several upper and lower bounds for the <span><math><mi>p</mi></math></span>-torsional rigidity. Our methods are mostly based on novel surgery principles. As an application, we also find some new estimates on the bottom of the spectrum of the <span><math><mi>p</mi></math></span>-Laplacian with Dirichlet conditions, thus complementing some results recently obtained in Mazón and Toledo (2023) in a more general setting. Finally, we prove a Kohler–Jobin inequality for combinatorial graphs (for <span><math><mrow><mi>p</mi><mo>=</mo><mn>2</mn></mrow></math></span>): to the best of our knowledge, graphs thus become the third ambient where a Kohler–Jobin inequality is known to hold.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"251 ","pages":"Article 113694"},"PeriodicalIF":1.3,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142662493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 existence for some fully nonlinear equations of Krylov-type arising in conformal geometry 论保角几何中出现的一些克雷洛夫型全非线性方程的存在性

IF 1.3 2区数学

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-11-12 DOI: 10.1016/j.na.2024.113709

Ya Ding, Yan He, Jun Liu

引用次数: 0

Optimal decay and regularity for a Thomas–Fermi type variational problem 托马斯-费米型变分问题的最优衰减和正则性

IF 1.3 2区数学

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-11-12 DOI: 10.1016/j.na.2024.113698

Damiano Greco

引用次数: 0

Blow-up estimates and a priori bounds for the positive solutions of a class of superlinear indefinite elliptic problems 一类超线性不定椭圆问题正解的膨胀估计和先验边界

IF 1.3 2区数学

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-11-12 DOI: 10.1016/j.na.2024.113693

Julián López-Gómez , Juan Carlos Sampedro

引用次数: 0

p-Wasserstein barycenters P-Waterstone Barycenters

IF 1.3 2区数学

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-11-12 DOI: 10.1016/j.na.2024.113687

Camilla Brizzi , Gero Friesecke , Tobias Ried

{"title":"p-Wasserstein barycenters","authors":"Camilla Brizzi , Gero Friesecke , Tobias Ried","doi":"10.1016/j.na.2024.113687","DOIUrl":"10.1016/j.na.2024.113687","url":null,"abstract":"<div><div>We study barycenters of <span><math><mi>N</mi></math></span> probability measures on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> with respect to the <span><math><mi>p</mi></math></span>-Wasserstein metric (<span><math><mrow><mn>1</mn><mo><</mo><mi>p</mi><mo><</mo><mi>∞</mi></mrow></math></span>). We prove that</div><div>– <span><math><mi>p</mi></math></span>-Wasserstein barycenters of absolutely continuous measures are unique, and again absolutely continuous</div><div>– <span><math><mi>p</mi></math></span>-Wasserstein barycenters admit a multi-marginal formulation</div><div>– the optimal multi-marginal plan is unique and of Monge form if the marginals are</div><div>absolutely continuous, and its support has an explicit parametrization as a graph over any</div><div>marginal space. This extends the Agueh–Carlier theory of Wasserstein barycenters <span><span>[1]</span></span> to exponents <span><math><mrow><mi>p</mi><mo>≠</mo><mn>2</mn></mrow></math></span>. A key ingredient is a quantitative injectivity estimate for the (highly non-injective) map from <span><math><mi>N</mi></math></span>-point configurations to their <span><math><mi>p</mi></math></span>-barycenter on the support of an optimal multi-marginal plan. We also discuss the statistical meaning of <span><math><mi>p</mi></math></span>-Wasserstein barycenters in one dimension.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"251 ","pages":"Article 113687"},"PeriodicalIF":1.3,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142662494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Measures in the dual of BV: perimeter bounds and relations with divergence-measure fields BV对偶中的度量：周界以及与发散度量场的关系

IF 1.3 2区数学

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-11-06 DOI: 10.1016/j.na.2024.113686

Giovanni E. Comi , Gian Paolo Leonardi

{"title":"Measures in the dual of BV: perimeter bounds and relations with divergence-measure fields","authors":"Giovanni E. Comi , Gian Paolo Leonardi","doi":"10.1016/j.na.2024.113686","DOIUrl":"10.1016/j.na.2024.113686","url":null,"abstract":"<div><div>We analyze some properties of the measures in the dual of the space <span><math><mrow><mi>B</mi><mi>V</mi></mrow></math></span>, by considering (signed) Radon measures satisfying a perimeter bound condition, which means that the absolute value of the measure of a set is controlled by the perimeter of the set itself, and whose total variations also belong to the dual of <span><math><mrow><mi>B</mi><mi>V</mi></mrow></math></span>. We exploit and refine the results of Cong Phuc and Torres (2017), in particular exploring the relation with divergence-measure fields and proving the stability of the perimeter bound from sets to <span><math><mrow><mi>B</mi><mi>V</mi></mrow></math></span> functions under a suitable approximation of the given measure. As an important tool, we obtain a refinement of Anzellotti-Giaquinta approximation for <span><math><mrow><mi>B</mi><mi>V</mi></mrow></math></span> functions, which is of separate interest in itself and, in the context of Anzellotti’s pairing theory for divergence-measure fields, implies a new way of approximating <span><math><mi>λ</mi></math></span>-pairings, as well as new bounds for their total variation. These results are also relevant due to their application in the study of weak solutions to the non-parametric prescribed mean curvature equation with measure data, which is explored in a subsequent work.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"251 ","pages":"Article 113686"},"PeriodicalIF":1.3,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142592583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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