1. Regularity for a class of integral functionals.
- Author
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Shuoyang, Li, Meng, Gao, and Hongya, Gao
- Abstract
This paper deals with regularity properties for variational integrals with the splitting structure of the form J(u,Ω)=∫Ω∑i=1n+1fi(x,Dui)+gi(x,(adjnDu)i)dx,$$\begin{equation*} \hspace*{59pt}{\cal J} (u,\Omega) = \int _{\Omega } \sum _{i=1}^{n+1} {\left\lbrace f^{i}(x,Du^{i})+ g^{i}(x,({\rm adj} _{n}Du)^{i}) \right\rbrace} dx, \end{equation*}$$where u=(u1,u2,…,un+1):Ω⊂Rn→Rn+1$u=(u^1,u^2, \ldots, u^{n+1}):\Omega \subset \mathbb {R}^n \rightarrow \mathbb {R}^{n+1}$, adjnDu∈Rn+1${\rm adj}_n Du \in \mathbb {R}^{n+1}$ is the adjugate matrix of order n$n$, and fi:Ω×Rn→R$f^i:\Omega \times \mathbb {R}^{n} \rightarrow \mathbb {R}$, gi:Ω×R→R$g^i:\Omega \times \mathbb {R} \rightarrow \mathbb {R}$, i=1,2,…,n+1$i=1,2, \ldots, n+1$, are Carathéodory functions satisfying suitable structural conditions. Local integrability, local boundedness, and local Hölder continuity for local minimizers are derived. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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