Mathematical Journal of Ibaraki University
Remarks on Kato's inequality when pu is a measure
Xiaojing LiuToshio Horiuchi
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Volume 48 (2016) Pages 45-61

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Abstract

Let Ω be a bounded domain of RN (N ≥ 1). In this article, we shall study Kato'’s inequality when ∆pu is a measure, where ∆pu denotes a p-Laplace operator with 1 < p < ∞. The classical Kato'’s inequality for a Laplacian asserts that given any function u L1loc(Ω) such that ∆uL1loc(Ω), then ∆(u+) is a Radon measure and the following holds: ∆(u+) ≥ χ[u ≥ 0]u in D(Ω). Our main result extends Kato’'s inequality to the case where ∆pu is a Radon measures on Ω. We also establish the inverse maximum principle for ∆p.

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© 2016 Department of Mathematics, Faculty of Science, Ibaraki University
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