Mathematical Journal of Ibaraki University
Online ISSN : 1883-4353
Print ISSN : 1343-3636
ISSN-L : 1343-3636
Kato's inequalities for admissible functions to quasilinear elliptic operators A
Xiaojing LiuToshio Horiuchi
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2019 Volume 51 Pages 49-64

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Abstract

Let 1 < p < ∞ and let Ω be a bounded domain of RN (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.

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© 2019 Department of Mathematics, Faculty of Science, Ibaraki University
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