Partial Differential Equations
Kato's inequality when Δu is a measure
Comptes Rendus. Mathématique, Volume 338 (2004) no. 8, pp. 599-604.

We extend the classical version of Kato's inequality in order to allow functions uL1loc such that Δu is a Radon measure. This inequality has been recently applied by Brezis, Marcus, and Ponce to study the existence of solutions of the nonlinear equation −Δu+g(u)=μ, where μ is a measure and $g\phantom{\rule{1.69998pt}{0ex}}:ℝ\to ℝ$ is a nondecreasing continuous function.

Nous étendons l'inégalité de Kato classique à des fonctions uL1loc telles que Δu est une mesure de Radon. Cette inégalité a été récemment utilisée par Brezis, Marcus et Ponce pour étudier l'existence de solutions de l'équation elliptique non linéaire −Δu+g(u)=μ, où μ est une mesure et $g\phantom{\rule{1.69998pt}{0ex}}:ℝ\to ℝ$ est une fonction croissante et continue.

Accepted:
Published online:
DOI: 10.1016/j.crma.2003.12.032
Brezis, Haı̈m 1, 2; Ponce, Augusto C. 1, 2

1 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, BC 187, 4, pl. Jussieu, 75252 Paris cedex 05, France
2 Rutgers University, Department of Math., Hill Center, Busch Campus, 110 Frelinghuysen Rd, Piscataway, NJ 08854, USA
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Brezis, Haı̈m; Ponce, Augusto C. Kato's inequality when Δu is a measure. Comptes Rendus. Mathématique, Volume 338 (2004) no. 8, pp. 599-604. doi : 10.1016/j.crma.2003.12.032. http://www.numdam.org/articles/10.1016/j.crma.2003.12.032/

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