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Advances in Calculus of Variations最新文献

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Révolution et contre-révolution fr 革命与反革命
3区 数学
Advances in Calculus of Variations Pub Date : 2023-10-12 DOI: 10.4000/variations.2339
Leonore Bazinek
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引用次数: 0
La Théorie critique en tant que révolution permanente 批判理论是一场永久的革命
3区 数学
Advances in Calculus of Variations Pub Date : 2023-10-12 DOI: 10.4000/variations.2340
Oskar Negt
{"title":"La Théorie critique en tant que révolution permanente","authors":"Oskar Negt","doi":"10.4000/variations.2340","DOIUrl":"https://doi.org/10.4000/variations.2340","url":null,"abstract":"","PeriodicalId":49276,"journal":{"name":"Advances in Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136014571","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
Minimizing movements for anisotropic and inhomogeneous mean curvature flows 各向异性和非均匀平均曲率流的最小运动
3区 数学
Advances in Calculus of Variations Pub Date : 2023-10-04 DOI: 10.1515/acv-2022-0102
Antonin Chambolle, Daniele de Gennaro, Massimiliano Morini
{"title":"Minimizing movements for anisotropic and inhomogeneous mean curvature flows","authors":"Antonin Chambolle, Daniele de Gennaro, Massimiliano Morini","doi":"10.1515/acv-2022-0102","DOIUrl":"https://doi.org/10.1515/acv-2022-0102","url":null,"abstract":"Abstract In this paper we address anisotropic and inhomogeneous mean curvature flows with forcing and mobility, and show that the minimizing movements scheme converges to level set/viscosity solutions and to distributional solutions à la Luckhaus–Sturzenhecker to such flows, the latter result holding in low dimension and conditionally to the convergence of the energies. By doing so we generalize recent works concerning the evolution by mean curvature by removing the hypothesis of translation invariance, which in the classical theory allows one to simplify many arguments.","PeriodicalId":49276,"journal":{"name":"Advances in Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135547527","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: 1
Wolff potentials and local behavior of solutions to elliptic problems with Orlicz growth and measure data 具有Orlicz增长和测量数据的椭圆型问题解的Wolff势和局部行为
3区 数学
Advances in Calculus of Variations Pub Date : 2023-10-04 DOI: 10.1515/acv-2023-0005
Iwona Chlebicka, Flavia Giannetti, Anna Zatorska-Goldstein
{"title":"Wolff potentials and local behavior of solutions to elliptic problems with Orlicz growth and measure data","authors":"Iwona Chlebicka, Flavia Giannetti, Anna Zatorska-Goldstein","doi":"10.1515/acv-2023-0005","DOIUrl":"https://doi.org/10.1515/acv-2023-0005","url":null,"abstract":"Abstract We establish pointwise bounds expressed in terms of a nonlinear potential of a generalized Wolff type for <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">𝒜</m:mi> </m:math> {{mathcal{A}}} -superharmonic functions with nonlinear operator <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi mathvariant=\"script\">𝒜</m:mi> <m:mo>:</m:mo> <m:mrow> <m:mrow> <m:mi mathvariant=\"normal\">Ω</m:mi> <m:mo>×</m:mo> <m:msup> <m:mi>ℝ</m:mi> <m:mi>n</m:mi> </m:msup> </m:mrow> <m:mo>→</m:mo> <m:msup> <m:mi>ℝ</m:mi> <m:mi>n</m:mi> </m:msup> </m:mrow> </m:mrow> </m:math> {{mathcal{A}}:Omegatimes{mathbb{R}^{n}}to{mathbb{R}^{n}}} having measurable dependence on the spacial variable and Orlicz growth with respect to the last variable. The result is sharp as the same potential controls estimates from above and from below. Applying it we provide a bunch of precise regularity results including continuity and Hölder continuity for solutions to problems involving measures that satisfy conditions expressed in the natural scales. Finally, we give a variant of Hedberg–Wolff theorem on characterization of the dual of the Orlicz space.","PeriodicalId":49276,"journal":{"name":"Advances in Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135549134","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
Frontmatter 头版头条
3区 数学
Advances in Calculus of Variations Pub Date : 2023-10-01 DOI: 10.1515/acv-2023-frontmatter4
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引用次数: 0
No breathers theorem for noncompact harmonic Ricci flows with asymptotically nonnegative Ricci curvature 具有渐近非负Ricci曲率的非紧调和Ricci流的无呼吸定理
IF 1.7 3区 数学
Advances in Calculus of Variations Pub Date : 2023-07-25 DOI: 10.1515/acv-2023-0003
Jiarui Chen, Qun Chen
{"title":"No breathers theorem for noncompact harmonic Ricci flows with asymptotically nonnegative Ricci curvature","authors":"Jiarui Chen, Qun Chen","doi":"10.1515/acv-2023-0003","DOIUrl":"https://doi.org/10.1515/acv-2023-0003","url":null,"abstract":"Abstract By using the monotonicity of the log Sobolev functionals, we prove a no breathers theorem for noncompact harmonic Ricci flows under conditions on infimum of log Sobolev functionals and curvatures. As an application, we obtain a no breathers theorem for noncompact harmonic Ricci flows with asymptotically nonnegative Ricci curvature.","PeriodicalId":49276,"journal":{"name":"Advances in Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46817241","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
Frontmatter 头版头条
3区 数学
Advances in Calculus of Variations Pub Date : 2023-07-01 DOI: 10.1515/acv-2023-frontmatter3
{"title":"Frontmatter","authors":"","doi":"10.1515/acv-2023-frontmatter3","DOIUrl":"https://doi.org/10.1515/acv-2023-frontmatter3","url":null,"abstract":"","PeriodicalId":49276,"journal":{"name":"Advances in Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135364084","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
Higher order Ambrosio–Tortorelli scheme with non-negative spatially dependent parameters 具有非负空间相关参数的高阶Ambrosio–Tortorelli格式
IF 1.7 3区 数学
Advances in Calculus of Variations Pub Date : 2023-06-27 DOI: 10.1515/acv-2021-0071
Irene Fonseca, Pan Liu, Xin Yang Lu
{"title":"Higher order Ambrosio–Tortorelli scheme with non-negative spatially dependent parameters","authors":"Irene Fonseca, Pan Liu, Xin Yang Lu","doi":"10.1515/acv-2021-0071","DOIUrl":"https://doi.org/10.1515/acv-2021-0071","url":null,"abstract":"Abstract The Ambrosio–Tortorelli approximation scheme with weighted underlying metric is investigated. It is shown that it Γ-converges to a Mumford–Shah image segmentation functional depending on the weight ω ⁢ d ⁢ x {omega,dx} , where ω is a special function of bounded variation, and on its values at the jumps.","PeriodicalId":49276,"journal":{"name":"Advances in Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42236082","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
On isosupremic vectorial minimisation problems in L ∞ with general nonlinear constraints 具有一般非线性约束的L∞中的同调向量最小化问题
IF 1.7 3区 数学
Advances in Calculus of Variations Pub Date : 2023-06-01 DOI: 10.1515/acv-2022-0068
E. Clark, Nikos Katzourakis
{"title":"On isosupremic vectorial minimisation problems in L ∞ with general nonlinear constraints","authors":"E. Clark, Nikos Katzourakis","doi":"10.1515/acv-2022-0068","DOIUrl":"https://doi.org/10.1515/acv-2022-0068","url":null,"abstract":"Abstract We study minimisation problems in L ∞ {L^{infty}} for general quasiconvex first order functionals, where the class of admissible mappings is constrained by the sublevel sets of another supremal functional and by the zero set of a nonlinear operator. Examples of admissible operators include those expressing pointwise, unilateral, integral isoperimetric, elliptic quasilinear differential, Jacobian and null Lagrangian constraints. Via the method of L p {L^{p}} approximations as p → ∞ {ptoinfty} , we illustrate the existence of a special L ∞ {L^{infty}} minimiser which solves a divergence PDE system involving certain auxiliary measures as coefficients. This system can be seen as a divergence form counterpart of the Aronsson PDE system which is associated with the constrained L ∞ {L^{infty}} variational problem.","PeriodicalId":49276,"journal":{"name":"Advances in Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47685576","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: 2
A flow approach to the prescribed Gaussian curvature problem in ℍ𝑛+1 中规定高斯曲率问题的一种流方法ℍ𝑛+1.
IF 1.7 3区 数学
Advances in Calculus of Variations Pub Date : 2023-05-06 DOI: 10.1515/acv-2022-0033
Haizhong Li, Ruijia Zhang
{"title":"A flow approach to the prescribed Gaussian curvature problem in ℍ𝑛+1","authors":"Haizhong Li, Ruijia Zhang","doi":"10.1515/acv-2022-0033","DOIUrl":"https://doi.org/10.1515/acv-2022-0033","url":null,"abstract":"Abstract In this paper, we study the following prescribed Gaussian curvature problem: K = f ~ ⁢ ( θ ) ϕ ⁢ ( ρ ) α − 2 ⁢ ϕ ⁢ ( ρ ) 2 + | ∇ ¯ ⁢ ρ | 2 , K=frac{tilde{f}(theta)}{phi(rho)^{alpha-2}sqrt{phi(rho)^{2}+lvertoverline{nabla}rhorvert^{2}}}, a generalization of the Alexandrov problem ( α = n + 1 alpha=n+1 ) in hyperbolic space, where f ~ tilde{f} is a smooth positive function on S n mathbb{S}^{n} , 𝜌 is the radial function of the hypersurface, ϕ ⁢ ( ρ ) = sinh ⁡ ρ phi(rho)=sinhrho and 𝐾 is the Gauss curvature. By a flow approach, we obtain the existence and uniqueness of solutions to the above equations when α ≥ n + 1 alphageq n+1 . Our argument provides a parabolic proof in smooth category for the Alexandrov problem in H n + 1 mathbb{H}^{n+1} . We also consider the cases 2 < α ≤ n + 1 2<alphaleq n+1 under the evenness assumption of f ~ tilde{f} and prove the existence of solutions to the above equations.","PeriodicalId":49276,"journal":{"name":"Advances in Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48480192","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
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