Kato's inequalities for admissible functions to quasilinear elliptic operators A

Abstract

Let 1 < p < 1 and let Ω be a bounded domain of R N ( N (cid:21) 1). In this paper, we consider a class of second order quasilinear elliptic operators A in Ω including the p -Laplace operator ∆ p . First we establish various type of Kato’s inequalities for A when A u is a Radon measure. Then we prove the inverse maximum principle and describe the strong maximum principle. For this purpose it is crucial to introduce a notion of admissible class for the operator A and use it effectively. y