Abstract

Steiner symmetrizations of anisotropic integral functionals of multivariate calculus of variations defined on the set of compactly supported functions in the Sobolev class are studied. Applications of the results to embedding theorems for anisotropic Orlicz–Sobolev spaces are outlined, and lower bounds for the values of multidimensional variational problems are found.

中文翻译：

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对称性和积分不等式

摘要

研究了在 Sobolev 类紧支持函数集上定义的多元变分演算的各向异性积分泛函的 Steiner 对称化。概述了结果在各向异性 Orlicz-Sobolev 空间嵌入定理中的应用，并找到了多维变分问题的值的下界。