The Liouville theorems for elliptic equations with nonstandard growth

Tomasz  Adamowicz; Przemysław  Górka

doi:10.3934/cpaa.2015.14.2377

Article Contents

2015, Volume 14, Issue 6: 2377-2392. Doi: 10.3934/cpaa.2015.14.2377

This issue Previous Article Harnack inequality for degenerate elliptic equations and sum operators Next Article Symmetry of solutions to semilinear equations involving the fractional laplacian

The Liouville theorems for elliptic equations with nonstandard growth

Tomasz Adamowicz^1, and
Przemysław Górka^2,

1.
Institute of Mathematics of the Polish Academy of Sciences, 00-956 Warsaw, Poland
2.
Department of Mathematics and Information Sciences, Warsaw University of Technology, Ul. Koszykowa 75, 00-662 Warsaw, Poland

Received: January 31, 2015

Revised: May 31, 2015

Published: October 2015

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Abstract

We study solutions and supersolutions of homogeneous and nonhomogeneous $A$-harmonic equations with nonstandard growth in $\mathbb{R}^n$. Various Liouville-type theorems and nonexistence results are proved. The discussion is illustrated by a number of examples.

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Mathematics Subject Classification: Primary 35B53; Secondary: 35J92, 46E30.

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