Advances in Calculus of Variations最新文献_第2页

Non-local BV functions and a denoising model with L 1 fidelity 非局部 BV 函数和保真度为 L 1 的去噪模型

IF 1.7 3区数学

Advances in Calculus of Variations Pub Date : 2024-01-30 DOI: 10.1515/acv-2023-0082

Konstantinos Bessas, Giorgio Stefani

{"title":"Non-local BV functions and a denoising model with L 1 fidelity","authors":"Konstantinos Bessas, Giorgio Stefani","doi":"10.1515/acv-2023-0082","DOIUrl":"https://doi.org/10.1515/acv-2023-0082","url":null,"abstract":"We study a general total variation denoising model with weighted <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>L</m:mi> <m:mn>1</m:mn> </m:msup> </m:math> {L^{1}} fidelity, where the regularizing term is a non-local variation induced by a suitable (non-integrable) kernel K, and the approximation term is given by the <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>L</m:mi> <m:mn>1</m:mn> </m:msup> </m:math> {L^{1}} norm with respect to a non-singular measure with positively lower-bounded <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>L</m:mi> <m:mi mathvariant=\"normal\">∞</m:mi> </m:msup> </m:math> {L^{infty}} density. We provide a detailed analysis of the space of non-local <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>BV</m:mi> </m:math> mathrm{BV} functions with finite total K-variation, with special emphasis on compactness, Lusin-type estimates, Sobolev embeddings and isoperimetric and monotonicity properties of the K-variation and the associated K-perimeter. Finally, we deal with the theory of Cheeger sets in this non-local setting and we apply it to the study of the fidelity in our model.","PeriodicalId":49276,"journal":{"name":"Advances in Calculus of Variations","volume":"1 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139586296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Quasiconformal, Lipschitz, and BV mappings in metric spaces 度量空间中的准共形、Lipschitz 和 BV 映射

IF 1.7 3区数学

Advances in Calculus of Variations Pub Date : 2024-01-12 DOI: 10.1515/acv-2022-0071

Panu Lahti

引用次数: 0

Generalized minimizing movements for the varifold Canham–Helfrich flow 变分卡纳姆-赫尔弗里希流的广义最小化运动

IF 1.7 3区数学

Advances in Calculus of Variations Pub Date : 2024-01-12 DOI: 10.1515/acv-2022-0056

Katharina Brazda, Martin Kružík, Ulisse Stefanelli

引用次数: 0

Effective quasistatic evolution models for perfectly plastic plates with periodic microstructure: The limiting regimes 具有周期性微观结构的完全塑性板材的有效准静态演化模型：极限状态

IF 1.7 3区数学

Advances in Calculus of Variations Pub Date : 2024-01-11 DOI: 10.1515/acv-2023-0020

Marin Bužančić, Elisa Davoli, Igor Velčić

引用次数: 0

Monotonicity of entire solutions to reaction-diffusion equations involving fractional p-Laplacian 涉及分数 p-Laplacian 的反应扩散方程全解的单调性

IF 1.7 3区数学

Advances in Calculus of Variations Pub Date : 2024-01-10 DOI: 10.1515/acv-2022-0109

Qing Guo

引用次数: 0

Asymptotic analysis of single-slip crystal plasticity in the limit of vanishing thickness and rigid elasticity 厚度和刚性弹性消失极限下单滑晶塑性的渐近分析

IF 1.7 3区数学

Advances in Calculus of Variations Pub Date : 2024-01-10 DOI: 10.1515/acv-2023-0009

Dominik Engl, Stefan Krömer, Martin Kružík

引用次数: 0

Least energy solutions for affine p-Laplace equations involving subcritical and critical nonlinearities 涉及亚临界和临界非线性的仿射 p-Laplace 方程的最小能量解

IF 1.7 3区数学

Advances in Calculus of Variations Pub Date : 2024-01-10 DOI: 10.1515/acv-2022-0050

Edir Júnior Ferreira Leite, Marcos Montenegro

{"title":"Least energy solutions for affine p-Laplace equations involving subcritical and critical nonlinearities","authors":"Edir Júnior Ferreira Leite, Marcos Montenegro","doi":"10.1515/acv-2022-0050","DOIUrl":"https://doi.org/10.1515/acv-2022-0050","url":null,"abstract":"The paper is concerned with Lane–Emden and Brezis–Nirenberg problems involving the affine <jats:italic>p</jats:italic>-Laplace nonlocal operator <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msubsup> <m:mi mathvariant=\"normal\">Δ</m:mi> <m:mi>p</m:mi> <m:mi mathvariant=\"script\">𝒜</m:mi> </m:msubsup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_acv-2022-0050_eq_0160.png\" /> <jats:tex-math>{Delta_{p}^{cal A}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, which has been introduced in [J. Haddad, C. H. Jiménez and M. Montenegro, From affine Poincaré inequalities to affine spectral inequalities, Adv. Math. 386 2021, Article ID 107808] driven by the affine <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>L</m:mi> <m:mi>p</m:mi> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_acv-2022-0050_eq_0140.png\" /> <jats:tex-math>{L^{p}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> energy <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi mathvariant=\"script\">ℰ</m:mi> <m:mrow> <m:mi>p</m:mi> <m:mo>,</m:mo> <m:mi mathvariant=\"normal\">Ω</m:mi> </m:mrow> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_acv-2022-0050_eq_0333.png\" /> <jats:tex-math>{{cal E}_{p,Omega}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> from convex geometry due to [E. Lutwak, D. Yang and G. Zhang, Sharp affine <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>L</m:mi> <m:mi>p</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_acv-2022-0050_eq_0108.png\" /> <jats:tex-math>L_{p}</jats:tex-math> </jats:alternatives> </jats:inline-formula> Sobolev inequalities, J. Differential Geom. 62 2002, 1, 17–38]. We are particularly interested in the existence and nonexistence of positive <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>C</m:mi> <m:mn>1</m:mn> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_acv-2022-0050_eq_0128.png\" /> <jats:tex-math>{C^{1}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> solutions of least energy type. Part of the main difficulties are caused by the absence of convexity of <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi mathvariant=\"script\">ℰ</m:mi> <m:mrow> <m:mi>p</m:mi> <m:mo>,</m:mo> <m:mi mathvariant=\"normal\">Ω</m:mi> </m:mrow> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_acv-2022-0050_eq_0333.png\" /> <jats:tex-math>{","PeriodicalId":49276,"journal":{"name":"Advances in Calculus of Variations","volume":"118 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139421631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 2+1-convex hull of a~finite set 无穷集的 2+1 凸体

IF 1.7 3区数学

Advances in Calculus of Variations Pub Date : 2024-01-01 DOI: 10.1515/acv-2023-0077

Pablo Angulo, Carlos García-Gutiérrez

{"title":"The 2+1-convex hull of a~finite set","authors":"Pablo Angulo, Carlos García-Gutiérrez","doi":"10.1515/acv-2023-0077","DOIUrl":"https://doi.org/10.1515/acv-2023-0077","url":null,"abstract":"Rank-one convexity is a weak form of convexity related to convex integration and the elusive notion of quasiconvexity, but more amenable both in theory and practice. However, exact algorithms for computing the rank one convex hull of a finite set are only known for some special cases of separate convexity with a finite number of directions. Both inner approximations either with laminates or <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>T</m:mi> <m:mn>4</m:mn> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_acv-2023-0077_eq_0331.png\" /> <jats:tex-math>{T_{4}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>’s and outer approximations through polyconvexity are known to be insufficient in general. We study <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msup> <m:mi>ℝ</m:mi> <m:mn>2</m:mn> </m:msup> <m:mo>⊕</m:mo> <m:mi>ℝ</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_acv-2023-0077_eq_0351.png\" /> <jats:tex-math>{mathbb{R}^{2}oplusmathbb{R}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-separately convex hulls of finite sets, which is a special case of rank-one convexity with infinitely many directions in which <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>T</m:mi> <m:mn>4</m:mn> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_acv-2023-0077_eq_0331.png\" /> <jats:tex-math>{T_{4}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>’s are known not to capture the rank one convex hull. When <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>ℝ</m:mi> <m:mn>3</m:mn> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_acv-2023-0077_eq_0353.png\" /> <jats:tex-math>{mathbb{R}^{3}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> is identified with a subset of <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mn>2</m:mn> <m:mo>×</m:mo> <m:mn>3</m:mn> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_acv-2023-0077_eq_0130.png\" /> <jats:tex-math>{2times 3}</jats:tex-math> </jats:alternatives> </jats:inline-formula> matrices, it is known to correspond also to quasiconvexity. We propose new inner and outer approximations built upon systematic use of known results, and prove that they agree. The inner approximation allows to understand better the structure of the rank one convex hull. The outer approximation gives rise to a computational algorithm which, in some cases, computes the hull exactly, and in general builds a sequence that c","PeriodicalId":49276,"journal":{"name":"Advances in Calculus of Variations","volume":"21 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139077263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 sub-Riemannian maximum modulus theorem 亚黎曼最大模定理

IF 1.7 3区数学

Advances in Calculus of Variations Pub Date : 2024-01-01 DOI: 10.1515/acv-2023-0066

Federico Buseghin, Nicolò Forcillo, Nicola Garofalo

引用次数: 0

Symmetry and monotonicity of singular solutions to p-Laplacian systems involving a first order term 包含一阶项的p-拉普拉斯系统奇异解的对称性和单调性

IF 1.7 3区数学

Advances in Calculus of Variations Pub Date : 2023-11-29 DOI: 10.1515/acv-2023-0043

Stefano Biagi, Francesco Esposito, Luigi Montoro, Eugenio Vecchi

引用次数: 1