KATO'S INEQUALITY UP TO THE BOUNDARY-Reference-Cited by-同舟云学术

KATO'S INEQUALITY UP TO THE BOUNDARY

Published:2008-12 Issue:06 Volume:10 Page:1217-1241
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

BREZIS HAÏM¹²,PONCE AUGUSTO C.³

Affiliation:

1. Department of Mathematics, Rutgers University, Hill Center, Busch Campus, 110 Frelinghuysen Rd., Piscataway, NJ 08854, USA

2. Department of Mathematics, Technion, 32000 Haifa, Israel

3. Département de Mathématique, Université catholique de Louvain, Chemin du Cyclotron 2, 1348 Louvain-la-Neuve, Belgium

Abstract

We show that if Δu is a finite measure in Ω then, under suitable assumptions on u near ∂Ω, Δu+ is also a finite measure in Ω. We also study properties of the normal derivatives [Formula: see text] and [Formula: see text] on ∂Ω.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199708003241

Reference10 articles.

1. Oxford Mathematical Monographs;Ambrosio L.,2000

2. Inégalité de Kato et inégalité de Kato jusqu'au bord

3. H. Brezis, M. Marcus and A. C. Ponce, Mathematical Aspects of Nonlinear Dispersive Equations, Annals of Mathematics Studies 163, eds. J. Bourgain, C. Kenig and S. Klainerman (Princeton University Press, Princeton, NJ, 2007) pp. 55–110.

4. Kato's inequality when Δu is a measure

5. Studies in Advanced Mathematics;Evans L. C.,1992

Cited by 22 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Existence and regularity results for a perturbed quasilinear 1-biharmonic equation;Asian-European Journal of Mathematics;2024-06-19

2. Optimal existence, uniqueness and blow-up for a quasilinear diffusion equation with spatially inhomogeneous reaction;Journal of Mathematical Analysis and Applications;2024-05

3. Kato’s inequality for the strong $p(\cdot )$-Laplacian;Studia Mathematica;2023

4. An Agmon–Allegretto–Piepenbrink principle for Schrödinger operators;Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas;2022-07-13

5. Maximal and minimal weak solutions for elliptic problems with nonlinearity on the boundary;Electronic Research Archive;2022