Hiroshima Mathematical Journal

Elliptic equations with nonstandard growth involving measures

T. Lukkari

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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

Permanent link to this document
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.)

Keywords
nonstandard growth measure data superharmonic functions

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


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