On weighted estimates of solutions of nonlinear elliptic problems
Igor V. Skrypnik; Dmitry V. Larin
Mathematica Bohemica (1999)
- Volume: 124, Issue: 2-3, page 173-184
- ISSN: 0862-7959
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topSkrypnik, Igor V., and Larin, Dmitry V.. "On weighted estimates of solutions of nonlinear elliptic problems." Mathematica Bohemica 124.2-3 (1999): 173-184. <http://eudml.org/doc/248454>.
@article{Skrypnik1999,
abstract = {The paper is devoted to the estimate
u(x,k)Kk\{capp,w(F)pw(B(x,))\} 1p-1,
$2p<n$ for a solution of a degenerate nonlinear elliptic equation in a domain $\{B(x_0,1)\setminus F\}$, $F\subset B(x_0,d)=\lbrace x\in \mathbb \{R\}^n |x_0-x|<d\rbrace $, $d<\frac\{1\}\{2\}$, under the boundary-value conditions $u(x,k)=k$ for $x\in \partial F$, $ u(x,k)=0$ for $x\in \partial B(x_0,1)$ and where $0<\rho \le \mathop dist(x,F)$, $w(x)$ is a weighted function from some Muckenhoupt class, and $\mathop cap_\{p,w\}(F)$, $w(B(x,\rho ))$ are weighted capacity and measure of the corresponding sets.},
author = {Skrypnik, Igor V., Larin, Dmitry V.},
journal = {Mathematica Bohemica},
keywords = {degeneracy; Muckenhoupt class; pointwise estimate; nonlinear elliptic equation; capacity; a-priori estimate; degeneracy; Muckenhoupt class; pointwise estimate; nonlinear elliptic equation; capacity; a-priori estimate},
language = {eng},
number = {2-3},
pages = {173-184},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On weighted estimates of solutions of nonlinear elliptic problems},
url = {http://eudml.org/doc/248454},
volume = {124},
year = {1999},
}
TY - JOUR
AU - Skrypnik, Igor V.
AU - Larin, Dmitry V.
TI - On weighted estimates of solutions of nonlinear elliptic problems
JO - Mathematica Bohemica
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 124
IS - 2-3
SP - 173
EP - 184
AB - The paper is devoted to the estimate
u(x,k)Kk{capp,w(F)pw(B(x,))} 1p-1,
$2p<n$ for a solution of a degenerate nonlinear elliptic equation in a domain ${B(x_0,1)\setminus F}$, $F\subset B(x_0,d)=\lbrace x\in \mathbb {R}^n |x_0-x|<d\rbrace $, $d<\frac{1}{2}$, under the boundary-value conditions $u(x,k)=k$ for $x\in \partial F$, $ u(x,k)=0$ for $x\in \partial B(x_0,1)$ and where $0<\rho \le \mathop dist(x,F)$, $w(x)$ is a weighted function from some Muckenhoupt class, and $\mathop cap_{p,w}(F)$, $w(B(x,\rho ))$ are weighted capacity and measure of the corresponding sets.
LA - eng
KW - degeneracy; Muckenhoupt class; pointwise estimate; nonlinear elliptic equation; capacity; a-priori estimate; degeneracy; Muckenhoupt class; pointwise estimate; nonlinear elliptic equation; capacity; a-priori estimate
UR - http://eudml.org/doc/248454
ER -
References
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- Chanillo S., Wheeden R. L., 10.2307/2374351, Amer. J. Math. 107 (1985), 1191-1226. (1985) Zbl0575.42026MR0805809DOI10.2307/2374351
- Kufner A., Weighted Sobolev spaces, B.G.Teubner Verlag, Leipzig, 1980. (1980) Zbl0455.46034MR0664599
- Gutiérrez C. E., Nelson G. S., 10.1080/03605308808820555, Commun. Partial Differential Equations 13 (1988), no. 5, 635-649. (1988) MR0919445DOI10.1080/03605308808820555
- Leonardi S., Skrypnik I. I., Necessary condition for regularity of a boundary point for a degenerate quasilinear parabolic equations, Catania Univ., Catania, 1995, preprint. (1995)
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