Existence and convergence of positive weak solutions of -Δu= {Mathematical expression} in bounded domains of ℝn, n≥3

Frank Pacard

doi:10.1007/BF01191296

Existence and convergence of positive weak solutions of -Δu= {Mathematical expression} in bounded domains of ℝⁿ, n≥3

Frank Pacard

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

Abstract

For the equation -Δu= {Mathematical expression} in Ω ⊂ℝⁿ we prove the existence of positive weak solutions with prescribed singular set. We also prove the existence of sequences of weak solutions which converge weakly but not strongly in L^n/n-2(Ω)

Original language	English
Pages (from-to)	243-265
Number of pages	23
Journal	Calculus of Variations and Partial Differential Equations
Volume	1
Issue number	3
DOIs	https://doi.org/10.1007/BF01191296
Publication status	Published - 1 Aug 1993

Keywords

Mathematics subject classification: 35J60, (35J20, 53A30)

Access to Document

10.1007/BF01191296

Cite this

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title = "Existence and convergence of positive weak solutions of -Δu= \{Mathematical expression\} in bounded domains of ℝn, n≥3",

abstract = "For the equation -Δu= \{Mathematical expression\} in Ω ⊂ℝn we prove the existence of positive weak solutions with prescribed singular set. We also prove the existence of sequences of weak solutions which converge weakly but not strongly in Ln/n-2(Ω)",

keywords = "Mathematics subject classification: 35J60, (35J20, 53A30)",

author = "Frank Pacard",

year = "1993",

month = aug,

day = "1",

doi = "10.1007/BF01191296",

language = "English",

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pages = "243--265",

journal = "Calculus of Variations and Partial Differential Equations",

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TY - JOUR

T1 - Existence and convergence of positive weak solutions of -Δu= {Mathematical expression} in bounded domains of ℝn, n≥3

AU - Pacard, Frank

PY - 1993/8/1

Y1 - 1993/8/1

N2 - For the equation -Δu= {Mathematical expression} in Ω ⊂ℝn we prove the existence of positive weak solutions with prescribed singular set. We also prove the existence of sequences of weak solutions which converge weakly but not strongly in Ln/n-2(Ω)

AB - For the equation -Δu= {Mathematical expression} in Ω ⊂ℝn we prove the existence of positive weak solutions with prescribed singular set. We also prove the existence of sequences of weak solutions which converge weakly but not strongly in Ln/n-2(Ω)

KW - Mathematics subject classification: 35J60, (35J20, 53A30)

U2 - 10.1007/BF01191296

DO - 10.1007/BF01191296

M3 - Article

AN - SCOPUS:0000617144

SN - 0944-2669

VL - 1

SP - 243

EP - 265

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 3