Kato's inequality when Δ<i>u</i> is a measure

Haı̈m Brezis; Augusto C. Ponce

doi:10.1016/j.crma.2003.12.032

Partial Differential Equations

Kato's inequality when Δu is a measure

Presented by: Haïm Brezis

Haı̈m Brezis ^1,²; Augusto C. Ponce ^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

Comptes Rendus. Mathématique, Volume 338 (2004) no. 8, pp. 599-604.

Abstract
Résumé

We extend the classical version of Kato's inequality in order to allow functions u∈L¹_loc 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 $g : ℝ \to ℝ$ is a nondecreasing continuous function.

Nous étendons l'inégalité de Kato classique à des fonctions u∈L¹_loc 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 $g : ℝ \to ℝ$ est une fonction croissante et continue.

Received: 2003-12-17
Accepted: 2003-12-17
Published online: 2004-03-25

DOI: 10.1016/j.crma.2003.12.032

Author's affiliations:

Haı̈m Brezis ^{1, 2}; Augusto C. Ponce ^{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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     title = {Kato's inequality when {\ensuremath{\Delta}\protect\emph{u}} is a measure},
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     pages = {599--604},
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Haı̈m Brezis; Augusto C. Ponce. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.12.032/

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