THE VARIABLE EXPONENT DE GIORGI CLASS AND THE VARIABLE EXPONENT HÕLDER CONTINUITY

被引：0

作者：

Yuan, Ya-ru ^{[1
]}

Cui, Zhi-yuan ^{[1
]}

Zhao, Dun ^{[1
]}

机构：

[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2025年 / 24卷 / 01期

关键词：

variable exponent growth; De Giorgi classes; variable exponent H & ocirc; lder spaces; regularity of solutions; ELLIPTIC-EQUATIONS; REGULARITY; SPACES; FUNCTIONALS;

D O I：

10.3934/cpaa.2024073

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a bounded domain f2 in R n (n >= 2), we prove that the variable exponent De Giorgi class m ( x ) (f2, M, gamma, gamma 1 , 8) is a subset of the variable exponent H & ocirc;lder space C 0 , alpha ( x ) loc (f2). It gives an improvement for the earlier result, which states that m ( x ) (f2, M, gamma, gamma 1 , 8) subset of C 0 , alpha loc (f2), where alpha is a constant. This result can be applied to get C 0 , alpha ( x ) loc (f2) regularity for certain solutions of variational problems and nonlinear elliptic equations with variable exponents.

引用

页码：1 / 14

页数：14

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