广义增长条件下的边界正则性

IF 0.7 3区数学 Q2 MATHEMATICS

Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2019-01-07 DOI:10.4171/ZAA/1628

Petteri Harjulehto, P. Hästö

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引用次数: 36

摘要

我们研究了具有Sobolev边值的Dirichletφ-能量积分。函数φ推广了Orlicz增长。特殊情况包括可变指数增长和双相增长。我们证明了在满足弱容量肥胖条件的情况下，极小值在边界处是正则的。例如，如果边界是Lipschitz，则满足该条件。即使对于Orlicz空间，结果也是新的。

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Boundary Regularity under Generalized Growth Conditions

We study the Dirichlet φ-energy integral with Sobolev boundary values. The function φ has generalized Orlicz growth. Special cases include variable exponent and double phase growths. We show that minimizers are regular at the boundary provided a weak capacity fatness condition is satisfied. This condition is satisfies for instance if the boundary is Lipschitz. The results are new even for Orlicz spaces.

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来源期刊

Zeitschrift fur Analysis und ihre Anwendungen 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Analysis and its Applications aims at disseminating theoretical knowledge in the field of analysis and, at the same time, cultivating and extending its applications. To this end, it publishes research articles on differential equations and variational problems, functional analysis and operator theory together with their theoretical foundations and their applications – within mathematics, physics and other disciplines of the exact sciences.