Local boundedness for minimizers of variational integrals under anisotropic nonstandard growth conditions

被引：0

作者：

Feng, Zesheng ^{[1
]}

Zhang, Aiping ^{[1
]}

Gao, Hongya ^{[1
]}

机构：

[1] Hebei Univ, Coll Chem & Environm Sci, 180 Wusi Dong Rd, Lian Chi Dist 071002, Baoding, Peoples R China

来源：

CZECHOSLOVAK MATHEMATICAL JOURNAL | 2024年

关键词：

local boundedness; minimizer; variational integral; anisotropic growth; convex; polyconvex; REGULARITY;

D O I：

10.21136/CMJ.2024.0121-24

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1165 / 1184

页数：20

共 50 条

[31] The partial regularity for minimizers of splitting type variational integrals under general growth conditions II. The nonautonomous case
Breit D.
Journal of Mathematical Sciences, 2010, 166 (3) : 33 - 52
[32] Boundedness of solutions to variational problems under general growth conditions
Cianchi, A
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1997, 22 (9-10) : 1629 - 1646
[33] Boundedness of solutions for anisotropic degenerate elliptic equations with nonstandard growth
Cianci, Paolo
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 364 (02) : 395 - 403
[34] Partial regularity for local minimizers of splitting-type variational integrals
Bildhauer, M.
Fuchs, M.
ASYMPTOTIC ANALYSIS, 2007, 55 (1-2) : 33 - 47
[35] Regularity of Relaxed Minimizers of Quasiconvex Variational Integrals with (p, q)-growth
Thomas Schmidt
Archive for Rational Mechanics and Analysis, 2009, 193 : 311 - 337
[36] Regularity of ω-minimizers of quasi-convex variational integrals with polynomial growth
Duzaar, F
Kronz, M
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2002, 17 (2-3) : 139 - 152
[37] Regularity of Relaxed Minimizers of Quasiconvex Variational Integrals with (p, q)-growth
Schmidt, Thomas
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2009, 193 (02) : 311 - 337
[38] A regularity theory for scalar local minimizers of splitting-type variational integrals
Bildhauer, Michael
Fuchs, Martin
Zhong, Xiao
ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2007, 6 (03) : 385 - 404
[39] On the regularity of local minimizers of decomposable variational integrals on domains in R-2
Bildhauer, M.
Fuchs, M.
COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE, 2007, 48 (02): : 321 - 341
[40] Parabolic equations with anisotropic nonstandard growth conditions
Antontsev, S.
Shmarev, S.
FREE BOUNDARY PROBLEMS: THEORY AND APPLICATIONS, 2007, 154 : 33 - +

← 1 2 3 4 5 →