Symmetrization and Integral Inequalities

V. S. Klimov

P.G. Demidov Yaroslavl State University

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.

Keywords: symmetrization, function, space, inequality, integral, gradient.

UDC: 517.518

Received: 19.10.2022
Revised: 22.02.2023

DOI: 10.4213/mzm13768

 English version: Mathematical Notes, 2023, 114:2, 230–241

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