Orlicz capacities and applications to some existence questions for elliptic PDEs having measure data

Alberto Fiorenza; Alain Prignet

ESAIM: Control, Optimisation and Calculus of Variations (2003)

  • Volume: 9, page 317-341
  • ISSN: 1292-8119

Abstract

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We study the sequence u n , which is solution of - div ( a ( x , 𝔻 u n ) ) + Φ ' ' ( | u n | ) u n = f n + g n in Ω an open bounded set of 𝐑 N and u n = 0 on ∂ Ω , when f n tends to a measure concentrated on a set of null Orlicz-capacity. We consider the relation between this capacity and the N -function Φ , and prove a non-existence result.

How to cite

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Fiorenza, Alberto, and Prignet, Alain. "Orlicz capacities and applications to some existence questions for elliptic PDEs having measure data." ESAIM: Control, Optimisation and Calculus of Variations 9 (2003): 317-341. <http://eudml.org/doc/245900>.

@article{Fiorenza2003,
abstract = {We study the sequence $u_n$, which is solution of $-\operatorname\{div\}(a(x,\mathbb \{D\}u_n)) + \Phi ^\{\prime \prime \}(|u_n|)\,u_n= f_n+ g_n$ in $\Omega $ an open bounded set of $\{\mathbf \{R\}\}^N$ and $u_n= 0$ on $\partial \Omega $, when $f_n$ tends to a measure concentrated on a set of null Orlicz-capacity. We consider the relation between this capacity and the $N$-function $\Phi $, and prove a non-existence result.},
author = {Fiorenza, Alberto, Prignet, Alain},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {elliptic equation; Orlicz space; measure; capacity},
language = {eng},
pages = {317-341},
publisher = {EDP-Sciences},
title = {Orlicz capacities and applications to some existence questions for elliptic PDEs having measure data},
url = {http://eudml.org/doc/245900},
volume = {9},
year = {2003},
}

TY - JOUR
AU - Fiorenza, Alberto
AU - Prignet, Alain
TI - Orlicz capacities and applications to some existence questions for elliptic PDEs having measure data
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2003
PB - EDP-Sciences
VL - 9
SP - 317
EP - 341
AB - We study the sequence $u_n$, which is solution of $-\operatorname{div}(a(x,\mathbb {D}u_n)) + \Phi ^{\prime \prime }(|u_n|)\,u_n= f_n+ g_n$ in $\Omega $ an open bounded set of ${\mathbf {R}}^N$ and $u_n= 0$ on $\partial \Omega $, when $f_n$ tends to a measure concentrated on a set of null Orlicz-capacity. We consider the relation between this capacity and the $N$-function $\Phi $, and prove a non-existence result.
LA - eng
KW - elliptic equation; Orlicz space; measure; capacity
UR - http://eudml.org/doc/245900
ER -

References

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