Czechoslovak Mathematical Journal, Vol. 74, No. 4, pp. 1165-1184, 2024
Local boundedness for minimizers of variational integrals under anisotropic nonstandard growth conditions
Zesheng Feng, Aiping Zhang, Hongya Gao
Received March 23, 2024. Published online October 20, 2024.
Abstract: This paper deals with local boundedness for minimizers of vectorial integrals under anisotropic growth conditions by using De Giorgi's iterative method. We consider integral functionals with the first part of the integrand satisfying anisotropic growth conditions including a convex nondecreasing function $g$, and with the second part, a convex lower order term or a polyconvex lower order term. Local boundedness of minimizers is derived.
Keywords: local boundedness; minimizer; variational integral; anisotropic growth; convex; polyconvex
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Affiliations: Zesheng Feng, Aiping Zhang, Hongya Gao (corresponding author), College of Mathematics and Information Science, Hebei University, No. 180 Wusi Dong Road, Lian Chi District, Baoding, 071002, P. R. China. e-mail: fengzesheng0227@qq.com, zhangaiping015@163.com, ghy@hbu.cn
