Original scientific paper

Higher integrabilities and boundednesses for minimizers of weighted anisotropic integral functionals

Tingfu Feng ; Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi, China
Yan Dong ; Department of Applied Mathematics, Hubei University of Economics, Wuhan, Hubei, China

Abstract

We consider the weighted anisotropic integral functional $$I(u)=\int_{\Omega}f(x,Du(x))dx,$$ where $\Omega\subset R^n$ is a bounded open set, $u:\Omega\subset R^n \rightarrow R $, $f:\Omega \times R^n \rightarrow [0,+\infty) $ is a Carath\'{e}odory function satisfying$$ \sum_{i=1}^{n}v_{i}{|z_{i}|}^{p_{i}}\leq f(x,z)\leq c\left(1+\sum_{i=1}^{n}v_{i}{|z_{i}|}^{q_{i}}\right),$$\\in which $c>0 $ is a constant, $1

Keywords

weighted anisotropic integral functional; minimizer; higher integrability; boundedness

Hrčak ID:

215146

URI

https://hrcak.srce.hr/215146

Publication date:

19.4.2019.

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