## Hiroshima Mathematical Journal

### Elliptic equations with nonstandard growth involving measures

T. Lukkari

#### Abstract

We show that given a positive and finite Radon measure $\mu$, there is a $\Apx$ -superharmonic function $u$ which satisfies

$-\dive\A(x,Du)=\mu$

in the sense of distributions. Here $\A$ is an elliptic operator with $p(x)$-type nonstandard growth.

#### Article information

Source
Hiroshima Math. J., Volume 38, Number 1 (2008), 155-176.

Dates
First available in Project Euclid: 7 April 2008

https://projecteuclid.org/euclid.hmj/1207580349

Digital Object Identifier
doi:10.32917/hmj/1207580349

Mathematical Reviews number (MathSciNet)
MR2397384

Zentralblatt MATH identifier
1148.35034

Subjects
Primary: 35J70: Degenerate elliptic equations
Secondary: 35D05 31C45: Other generalizations (nonlinear potential theory, etc.)

#### Citation

Lukkari, T. Elliptic equations with nonstandard growth involving measures. Hiroshima Math. J. 38 (2008), no. 1, 155--176. doi:10.32917/hmj/1207580349. https://projecteuclid.org/euclid.hmj/1207580349