## Advances in Differential Equations

### Singular boundary value problems for nonlinear elliptic equations in nonsmooth domains

#### Abstract

Let $\Omega$ be a piecewise-regular domain in $\Bbb R^N$ and O an irregular point on its boundary $\partial \Omega$. We study under what conditions on $q$ any solution $u$ of (E) $-\Delta u + g(x,u)=0$ where $g$ has a $q$-power-like growth at infinity ($q>1$) which coincides on $\partial \Omega \setminus {\{\text{O}}\}$ with a continuous function defined on whole $\partial \Omega$, can be extended as a continuous function in $\bar \Omega$.

#### Article information

Source
Adv. Differential Equations, Volume 1, Number 6 (1996), 1075-1098.

Dates
First available in Project Euclid: 25 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366895245

Mathematical Reviews number (MathSciNet)
MR1409900

Zentralblatt MATH identifier
0863.35021

#### Citation

Fabbri, Jean; Veron, Laurent. Singular boundary value problems for nonlinear elliptic equations in nonsmooth domains. Adv. Differential Equations 1 (1996), no. 6, 1075--1098. https://projecteuclid.org/euclid.ade/1366895245