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Pointwise estimates of nonnegative subsolutions of quasilinear elliptic equations at irregular boundary points

Jan Malý

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 1, page 23-42
  • ISSN: 0010-2628

Abstract

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Let u be a weak solution of a quasilinear elliptic equation of the growth p with a measure right hand term μ . We estimate u ( z ) at an interior point z of the domain Ω , or an irregular boundary point z ∈ ∂ Ω , in terms of a norm of u , a nonlinear potential of μ and the Wiener integral of 𝐑 n ∖ Ω . This quantifies the result on necessity of the Wiener criterion.

How to cite

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Malý, Jan. "Pointwise estimates of nonnegative subsolutions of quasilinear elliptic equations at irregular boundary points." Commentationes Mathematicae Universitatis Carolinae 37.1 (1996): 23-42. <http://eudml.org/doc/247923>.

@article{Malý1996,
abstract = {Let $u$ be a weak solution of a quasilinear elliptic equation of the growth $p$ with a measure right hand term $\mu $. We estimate $u(z)$ at an interior point $z$ of the domain $\Omega $, or an irregular boundary point $z\in \partial \Omega $, in terms of a norm of $u$, a nonlinear potential of $\mu $ and the Wiener integral of $\mathbf \{R\}^n\setminus \Omega $. This quantifies the result on necessity of the Wiener criterion.},
author = {Malý, Jan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {elliptic equations; Wiener criterion; nonlinear potentials; measure data; measure data; Wiener integral; Wiener criterion},
language = {eng},
number = {1},
pages = {23-42},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Pointwise estimates of nonnegative subsolutions of quasilinear elliptic equations at irregular boundary points},
url = {http://eudml.org/doc/247923},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Malý, Jan
TI - Pointwise estimates of nonnegative subsolutions of quasilinear elliptic equations at irregular boundary points
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 1
SP - 23
EP - 42
AB - Let $u$ be a weak solution of a quasilinear elliptic equation of the growth $p$ with a measure right hand term $\mu $. We estimate $u(z)$ at an interior point $z$ of the domain $\Omega $, or an irregular boundary point $z\in \partial \Omega $, in terms of a norm of $u$, a nonlinear potential of $\mu $ and the Wiener integral of $\mathbf {R}^n\setminus \Omega $. This quantifies the result on necessity of the Wiener criterion.
LA - eng
KW - elliptic equations; Wiener criterion; nonlinear potentials; measure data; measure data; Wiener integral; Wiener criterion
UR - http://eudml.org/doc/247923
ER -

References

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