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 (2010)

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

Abstract

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We study the sequence un, which is solution of - div ( a ( x , u n ) ) + Φ ' ' ( | u n | ) u n = f n + g n in Ω an open bounded set of RN and un= 0 on ∂Ω, when fn 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 (2010): 317-341. <http://eudml.org/doc/90698>.

@article{Fiorenza2010,
abstract = { We study the sequence un, which is solution of $-\{\rm div\}(a(x,\{\nabla\}u_n)) + \Phi''(|u_n|)\,u_n= f_n+ g_n$ in Ω an open bounded set of RN and un= 0 on ∂Ω, when fn 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. },
author = {Fiorenza, Alberto, Prignet, Alain},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Elliptic equation; Orlicz space; measure; capacity.; elliptic equation; capacity},
language = {eng},
month = {3},
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/90698},
volume = {9},
year = {2010},
}

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
DA - 2010/3//
PB - EDP Sciences
VL - 9
SP - 317
EP - 341
AB - We study the sequence un, which is solution of $-{\rm div}(a(x,{\nabla}u_n)) + \Phi''(|u_n|)\,u_n= f_n+ g_n$ in Ω an open bounded set of RN and un= 0 on ∂Ω, when fn 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.
LA - eng
KW - Elliptic equation; Orlicz space; measure; capacity.; elliptic equation; capacity
UR - http://eudml.org/doc/90698
ER -

References

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