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Kato's Inequalities for Degenerate Quasilinear Elliptic Operators
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  • Journal title : Kyungpook mathematical journal
  • Volume 48, Issue 1,  2008, pp.15-24
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2008.48.1.015
 Title & Authors
Kato's Inequalities for Degenerate Quasilinear Elliptic Operators
Horiuchi, Toshio;
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 Abstract
Let and p > 1. Let be a domain of . In this article we shall establish Kato's inequalities for quasilinear degenerate elliptic operators of the form = divA(x,u) for , ), where is an admissible class and is a mapping satisfying some structural conditions. If p = 2 for example, then we have . Then we shall prove that (sgn u) and in D'() with . These inequalities are called Kato's inequalities provided that p = 2. The class of operators contains the so-called p-harmonic operators for .
 Keywords
Kato's inequality;p-harmonic operators;
 Language
English
 Cited by
 References
1.
J. Garcia-Cuerva and J. L. Rubio de Francia, Weighted norm inequalities and related Topics, North-Holland Mthematics Studies, 116(1985).

2.
T. Horiuchi, Some remarks on Kato's inequality, J. of Inequalities and applications., 6(2001), 29-36. crossref(new window)

3.
T. Kato, Schrodinger operators with singular potentials, Israel J. Math., 1 (1972), 135-148.