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 $$I(u)={\int }_{\mathrm{\Omega }}f(x,Du(x))dx,$$ where $\mathrm{\Omega }\subset R^n$ is a bounded open set, $u:\mathrm{\Omega }\subset R^n\to R$, $f:\mathrm{\Omega }\times R^n\to [0,+\mathrm{\infty })$ is a Carath\'{e}odory function satisfying$$\sum _{i=1}^n{v}_i{|z_i|}^{p_i}\le f(x,z)\le c(1+\sum _{i=1}^n{v}_i{|z_i|}^{q_i}),$$\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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