度量空间中非齐次增长泛函梯度流的弱解。

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Evolution Equations Pub Date : 2025-01-01 Epub Date: 2025-05-04 DOI:10.1007/s00028-025-01071-z

Wojciech Górny

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引用次数: 0

摘要

利用Gigli引入的度量度量空间中的一阶微分结构框架，定义了凸、下半连续和强制泛函梯度流的弱解概念。证明了它们的存在唯一性，并证明了它们也是变分解；特别地，这是变分解的存在性结果。然后，我们将此技术应用于非齐次增长泛函的梯度流。

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Weak solutions to gradient flows of functionals with inhomogeneous growth in metric spaces.

We use the framework of the first-order differential structure in metric measure spaces introduced by Gigli to define a notion of weak solution to gradient flows of convex, lower semicontinuous and coercive functionals. We prove their existence and uniqueness and show that they are also variational solutions; in particular, this is an existence result for variational solutions. Then, we apply this technique in the case of a gradient flow of a functional with inhomogeneous growth.

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来源期刊

Journal of Evolution Equations 数学-数学

CiteScore

2.30

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Evolution Equations (JEE) publishes high-quality, peer-reviewed papers on equations dealing with time dependent systems and ranging from abstract theory to concrete applications. Research articles should contain new and important results. Survey articles on recent developments are also considered as important contributions to the field. Particular topics covered by the journal are: Linear and Nonlinear Semigroups Parabolic and Hyperbolic Partial Differential Equations Reaction Diffusion Equations Deterministic and Stochastic Control Systems Transport and Population Equations Volterra Equations Delay Equations Stochastic Processes and Dirichlet Forms Maximal Regularity and Functional Calculi Asymptotics and Qualitative Theory of Linear and Nonlinear Evolution Equations Evolution Equations in Mathematical Physics Elliptic Operators