A priori regularity for weak solutions of some nonlinear elliptic equations

Frank Pacard

doi:10.1016/S0294-1449(16)30174-3

A priori regularity for weak solutions of some nonlinear elliptic equations

Frank Pacard

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

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Résumé

Let f(u) be some positive regular function bounded from above by u^{[Formula presented]}, in ℝ⁺. We derive some necessary and sufficient conditions, in order for all positive solutions to −Δu=f(u)∈L_loc ¹(ℝⁿ) to be regular.

langue originale	Anglais
Pages (de - à)	693-703
Nombre de pages	11
journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	11
Numéro de publication	6
Les DOIs	https://doi.org/10.1016/S0294-1449(16)30174-3
état	Publié - 1 nov. 1994

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10.1016/S0294-1449(16)30174-3

Contient cette citation

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title = "A priori regularity for weak solutions of some nonlinear elliptic equations",

abstract = "Let f(u) be some positive regular function bounded from above by u[Formula presented], in ℝ+. We derive some necessary and sufficient conditions, in order for all positive solutions to −Δu=f(u)∈Lloc 1(ℝn) to be regular.",

keywords = "35 J 20, 35 J 60, 53 A 30, Nonlinear Elliptic Equation, Regularity",

author = "Frank Pacard",

note = "Publisher Copyright: {\textcopyright} 2016 L'Association Publications de l'Institut Henri Poincar{\'e}",

year = "1994",

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AB - Let f(u) be some positive regular function bounded from above by u[Formula presented], in ℝ+. We derive some necessary and sufficient conditions, in order for all positive solutions to −Δu=f(u)∈Lloc 1(ℝn) to be regular.

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KW - 35 J 60

KW - 53 A 30

KW - Nonlinear Elliptic Equation

KW - Regularity

U2 - 10.1016/S0294-1449(16)30174-3

DO - 10.1016/S0294-1449(16)30174-3

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SN - 0294-1449

VL - 11

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JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

IS - 6

ER -

A priori regularity for weak solutions of some nonlinear elliptic equations

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