奇异非均质 (m, p)- 拉普拉斯方程的尖锐正则估计值

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis Pub Date : 2024-08-26 DOI:10.1007/s11118-024-10164-2

Pêdra D. S. Andrade, João Vitor da Silva, Giane C. Rampasso, Makson S. Santos

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引用次数: 0

摘要

在本文中，我们研究了一类双非线性演化 PDE。我们为荷尔德空间中的解建立了尖锐的正则性。证明基于几何切向法和本征缩放技术。我们的研究结果通过在慢速、正常和快速扩散状态下的统一处理，扩展并恢复了具有奇异特征的经典演化 PDEs 的结果。此外，我们还提供了某些非线性演化模型的应用，这些模型可能有其自身的数学意义。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Sharp Regularity Estimates for a Singular Inhomogeneous (m, p)-Laplacian Equation

In this paper, we investigate a class of doubly nonlinear evolutions PDEs. We establish sharp regularity for the solutions in Hölder spaces. The proof is based on the geometric tangential method and intrinsic scaling technique. Our findings extend and recover the results in the context of the classical evolution PDEs with singular signature via a unified treatment in the slow, normal and fast diffusion regimes. In addition, we provide some applications to certain nonlinear evolution models, which may have their own mathematical interest.

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来源期刊

Potential Analysis 数学-数学

CiteScore

2.20

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original papers dealing with potential theory and its applications, probability theory, geometry and functional analysis and in particular estimations of the solutions of elliptic and parabolic equations; analysis of semi-groups, resolvent kernels, harmonic spaces and Dirichlet forms; Markov processes, Markov kernels, stochastic differential equations, diffusion processes and Levy processes; analysis of diffusions, heat kernels and resolvent kernels on fractals; infinite dimensional analysis, Gaussian analysis, analysis of infinite particle systems, of interacting particle systems, of Gibbs measures, of path and loop spaces; connections with global geometry, linear and non-linear analysis on Riemannian manifolds, Lie groups, graphs, and other geometric structures; non-linear or semilinear generalizations of elliptic or parabolic equations and operators; harmonic analysis, ergodic theory, dynamical systems; boundary value problems, Martin boundaries, Poisson boundaries, etc.