Fine topology and quasilinear elliptic equations

Juha Heinonen; Terro Kilpeläinen; Olli Martio

Annales de l'institut Fourier (1989)

  • Volume: 39, Issue: 2, page 293-318
  • ISSN: 0373-0956

Abstract

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It is shown that the ( 1 , p ) -fine topology defined via a Wiener criterion is the coarsest topology making all supersolutions to the p -Laplace equation div ( | ∇ u | p - 2 ∇ u ) = 0 continuous. Fine limits of quasiregular and BLD mappings are also studied.

How to cite

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Heinonen, Juha, Kilpeläinen, Terro, and Martio, Olli. "Fine topology and quasilinear elliptic equations." Annales de l'institut Fourier 39.2 (1989): 293-318. <http://eudml.org/doc/74832>.

@article{Heinonen1989,
abstract = {It is shown that the $(1,p)$-fine topology defined via a Wiener criterion is the coarsest topology making all supersolutions to the $p$-Laplace equation\begin\{\}\{\rm div\}\,(\vert \nabla u\vert ^\{p-2\} \nabla u)=0\end\{\}continuous. Fine limits of quasiregular and BLD mappings are also studied.},
author = {Heinonen, Juha, Kilpeläinen, Terro, Martio, Olli},
journal = {Annales de l'institut Fourier},
keywords = {quasilinear; fine topology; Wiener criterion; supersolutions; p-Laplace equation; continuous; Fine limits},
language = {eng},
number = {2},
pages = {293-318},
publisher = {Association des Annales de l'Institut Fourier},
title = {Fine topology and quasilinear elliptic equations},
url = {http://eudml.org/doc/74832},
volume = {39},
year = {1989},
}

TY - JOUR
AU - Heinonen, Juha
AU - Kilpeläinen, Terro
AU - Martio, Olli
TI - Fine topology and quasilinear elliptic equations
JO - Annales de l'institut Fourier
PY - 1989
PB - Association des Annales de l'Institut Fourier
VL - 39
IS - 2
SP - 293
EP - 318
AB - It is shown that the $(1,p)$-fine topology defined via a Wiener criterion is the coarsest topology making all supersolutions to the $p$-Laplace equation\begin{}{\rm div}\,(\vert \nabla u\vert ^{p-2} \nabla u)=0\end{}continuous. Fine limits of quasiregular and BLD mappings are also studied.
LA - eng
KW - quasilinear; fine topology; Wiener criterion; supersolutions; p-Laplace equation; continuous; Fine limits
UR - http://eudml.org/doc/74832
ER -

References

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