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2005 Gradient estimates for anisotropic elliptic equations
Gary M. Lieberman
Adv. Differential Equations 10(7): 767-812 (2005).

Abstract

We study a class of elliptic equations with different degeneracies in different directions such as $$ \left( |u_x|^{m-2}u_x\right)_x + \left( |u_y|^{q-2}u_y\right)_y =0 $$ with unequal parameters $m$ and $q$, both greater than one. We show that any bounded solution of such an equation must have a bounded gradient. The ideas also apply to a much more general class of degenerate equations, which we describe in some detail.

Citation

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Gary M. Lieberman. "Gradient estimates for anisotropic elliptic equations." Adv. Differential Equations 10 (7) 767 - 812, 2005.

Information

Published: 2005
First available in Project Euclid: 18 December 2012

zbMATH: 1144.35388
MathSciNet: MR2152352

Subjects:
Primary: 35J60
Secondary: 35B45, 35B65, 35J70

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.10 • No. 7 • 2005
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