平面边界域p-Laplace型PDE解的Fatou型定理失效

IF 2.1 2区数学 Q1 MATHEMATICS

Communications in Partial Differential Equations Pub Date : 2021-09-10 DOI:10.1080/03605302.2022.2056704

M. Akman, Johnny M. Lewis, A. Vogel

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引用次数: 0

摘要

我们首先研究了p-拉普拉斯方程(称为p-调和函数)的解的Martin边界问题，然后利用我们的研究结果将Wolff关于p-调和函数的Fatou型定理失效的工作推广到p-调和函数的失效。我们讨论了我们的工作推广到p-拉普拉斯型PDE(称为-调和函数)的解。

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Failure of Fatou type theorems for solutions to PDE of p-Laplace type in domains with flat boundaries

Abstract Let denote Euclidean n space and given k a positive integer let be a k-dimensional plane with If we first study the Martin boundary problem for solutions to the p-Laplace equation (called p-harmonic functions) in relative to We then use the results from our study to extend the work of Wolff on the failure of Fatou type theorems for p-harmonic functions in to p-harmonic functions in when Finally, we discuss generalizations of our work to solutions of p-Laplace type PDE (called -harmonic functions).

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来源期刊

Communications in Partial Differential Equations 数学-数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal aims to publish high quality papers concerning any theoretical aspect of partial differential equations, as well as its applications to other areas of mathematics. Suitability of any paper is at the discretion of the editors. We seek to present the most significant advances in this central field to a wide readership which includes researchers and graduate students in mathematics and the more mathematical aspects of physics and engineering.