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

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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)∈L_loc ¹(ℝⁿ) to be regular.

Original language	English
Pages (from-to)	693-703
Number of pages	11
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	11
Issue number	6
DOIs	https://doi.org/10.1016/S0294-1449(16)30174-3
Publication status	Published - 1 Nov 1994

Keywords

35 J 20
35 J 60
53 A 30
Nonlinear Elliptic Equation
Regularity

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10.1016/S0294-1449(16)30174-3

Cite this

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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",

month = nov,

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doi = "10.1016/S0294-1449(16)30174-3",

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AU - Pacard, Frank

PY - 1994/11/1

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N2 - 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.

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.

KW - 35 J 20

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

M3 - Article

AN - SCOPUS:42149185223

SN - 0294-1449

VL - 11

SP - 693

EP - 703

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

Abstract

Keywords

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