Riemannian starshape and capacitary problems

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2025-03-23 DOI:10.1016/j.nonrwa.2025.104368

Kazuhiro Ishige , Paolo Salani , Asuka Takatsu

引用次数: 0

Abstract

We prove the Riemannian version of a classical Euclidean result: every level set of the capacitary potential of a starshaped ring is starshaped. In the Riemannian setting, we restrict ourselves to starshaped rings in a warped product of an open interval and the unit sphere. We also extend the result by replacing the Laplacian with the

q

-Laplacian.

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黎曼星形和电容问题

我们证明了一个经典欧几里得结果的黎曼版本：星形环的容势的每一水平集都是星形的。在黎曼环境中，我们将自己限制在开区间与单位球的弯曲积中的星形环。我们还通过用q-拉普拉斯替换拉普拉斯来扩展结果。

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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来源期刊

Nonlinear Analysis-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.