### A weak maximum principle for the linearized operator of $m$-Laplace equations with applications to a nondegeneracy result

Berardino Sciunzi

#### Abstract

We consider the Dirichlet problem for positive solutions of the equation $-\Delta_m (u) = f(u) \;$ in a bounded, smooth domain $\, \Omega$, with $f$ positive and locally Lipschitz continuous. We prove a weak maximum principle in small domains for the linearized operator that we exploit to prove a weak maximum principle for the linearized operator. We then consider the case $f(s)=s^q$ and prove a nondegeneracy result in weighted Sobolev spaces.

#### Article information

Source
Adv. Differential Equations Volume 10, Number 2 (2005), 223-240.

Dates
First available in Project Euclid: 18 December 2012

Sciunzi, Berardino. A weak maximum principle for the linearized operator of $m$-Laplace equations with applications to a nondegeneracy result. Adv. Differential Equations 10 (2005), no. 2, 223--240. https://projecteuclid.org/euclid.ade/1355867889