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

Abstract

Let 1 < p < ∞ and let Ω be a bounded domain of R^N (N ≥ 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 Au 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.