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September/October 2012 A priori estimates and reduction principles for quasilinear elliptic problems and applications
Lorenzo D'Ambrosio, Enzo Mitidieri
Adv. Differential Equations 17(9/10): 935-1000 (September/October 2012).

Abstract

Variants of Kato's inequality are proved for general quasilinear elliptic operators $L$. As an outcome we show that, dealing with Liouville theorems for coercive equations of the type \begin{equation*} Lu = f(x,u,{\nabla_{\!\!L}} u) \quad on\ \Omega\subset{{\mathbb{R}}^N} , \end{equation*} where $f$ is such that $f(x,t,\xi) \,t\ge 0$, the assumption that the possible solutions are nonnegative involves no loss of generality. Related consequences such as comparison principles and a priori bounds on solutions are also presented. An underlying structure throughout this work is the framework of Carnot groups.

Citation

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Lorenzo D'Ambrosio. Enzo Mitidieri. "A priori estimates and reduction principles for quasilinear elliptic problems and applications." Adv. Differential Equations 17 (9/10) 935 - 1000, September/October 2012.

Information

Published: September/October 2012
First available in Project Euclid: 17 December 2012

zbMATH: 1273.35138
MathSciNet: MR2985680

Subjects:
Primary: 35B45, 35B51, 35B53, 35J62, 35J70, 35R03

Rights: Copyright © 2012 Khayyam Publishing, Inc.

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Vol.17 • No. 9/10 • September/October 2012
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