具有粗糙数据的弱调和映射的Dirichlet问题

IF 2.1 2区数学 Q1 MATHEMATICS

Communications in Partial Differential Equations Pub Date : 2021-10-08 DOI:10.1080/03605302.2022.2056705

Gael Diebou Yomgne, H. Koch

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引用次数: 3

摘要

摘要研究了从域（上半空间或有界域）到光滑闭流形的弱调和映射。在任一类中规定小的狄利克雷数据，或者我们通过非变分方法建立所得边值问题的可解性。作为副产品，解被证明是局部光滑的。此外，我们证明了如果Ω是光滑的，并且通过扰动严格稳定的光滑调和映射来定界，则边界数据可以在底层拓扑中被选择得很大。

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Dirichlet problem for weakly harmonic maps with rough data

Abstract Weakly harmonic maps from a domain (the upper half-space or a bounded domain, ) into a smooth closed manifold are studied. Prescribing small Dirichlet data in either of the classes or we establish solvability of the resulting boundary value problems by means of a nonvariational method. As a by-product, solutions are shown to be locally smooth, Moreover, we show that boundary data can be chosen large in the underlying topologies if Ω is smooth and bounded by perturbing strictly stable smooth harmonic maps.

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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.