边界上有德里赫特区域的传输密度 BV 估计值

IF 2.1 2区数学 Q1 MATHEMATICS Calculus of Variations and Partial Differential Equations Pub Date : 2024-07-10 DOI:10.1007/s00526-024-02746-0

Samer Dweik

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引用次数: 0

摘要

在本文中，我们证明了二维质量输运问题中，在域、边界成本和质量分布的特定条件下，到边界的输运密度的BV正则性。此外，我们还通过一个反例证明了质量分布、边界和边界成本的平滑性并不意味着在某个 \(p>1\) 条件下输运密度是 \(W^{1,p}\)。

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BV estimates on the transport density with Dirichlet region on the boundary

In this paper, we prove BV regularity on the transport density in the mass transport problem to the boundary in two dimensions under certain conditions on the domain, the boundary cost and the mass distribution. Moreover, we show by a counter-example that the smoothness of the mass distribution, the boundary and the boundary cost does not imply that the transport density is \(W^{1,p}\), for some \(p>1\).

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来源期刊

Calculus of Variations and Partial Differential Equations 数学-数学

CiteScore

3.30

自引率

4.80%

发文量

224

审稿时长

6 months

期刊介绍： Calculus of variations and partial differential equations are classical, very active, closely related areas of mathematics, with important ramifications in differential geometry and mathematical physics. In the last four decades this subject has enjoyed a flourishing development worldwide, which is still continuing and extending to broader perspectives. This journal will attract and collect many of the important top-quality contributions to this field of research, and stress the interactions between analysts, geometers, and physicists. The field of Calculus of Variations and Partial Differential Equations is extensive; nonetheless, the journal will be open to all interesting new developments. Topics to be covered include: - Minimization problems for variational integrals, existence and regularity theory for minimizers and critical points, geometric measure theory - Variational methods for partial differential equations, optimal mass transportation, linear and nonlinear eigenvalue problems - Variational problems in differential and complex geometry - Variational methods in global analysis and topology - Dynamical systems, symplectic geometry, periodic solutions of Hamiltonian systems - Variational methods in mathematical physics, nonlinear elasticity, asymptotic variational problems, homogenization, capillarity phenomena, free boundary problems and phase transitions - Monge-Ampère equations and other fully nonlinear partial differential equations related to problems in differential geometry, complex geometry, and physics.