## Journal of the Mathematical Society of Japan

### Removable singularities for quasilinear degenerate elliptic equations with absorption term

Toshio HORIUCHI

#### Abstract

Let $N\geq 1$ and $p>1$. Let $F$ be a compact set and $\Omega$ be a bounded open set of $R^{N}$ satisfying $F\subset\Omega\subset R^{N}$. We define a generalized $p$-harmonic operator $L_{p}$ which is elliptic in $\Omega\backslash F$ and degenerated on $F$. We shall study the genuinely degenerate elliptic equations with absorption term. In connection with these equations we shall treat two topics in the present paper. Namely, the one is concerned with removable singularities of solutions and the other is the unique existence property of bounded solutions for the Dirichlet boundary problem.

#### Article information

Source
J. Math. Soc. Japan, Volume 53, Number 3 (2001), 513-540.

Dates
First available in Project Euclid: 9 June 2008

https://projecteuclid.org/euclid.jmsj/1213023721

Digital Object Identifier
doi:10.2969/jmsj/05330513

Mathematical Reviews number (MathSciNet)
MR1828967

Zentralblatt MATH identifier
1136.35392

#### Citation

HORIUCHI, Toshio. Removable singularities for quasilinear degenerate elliptic equations with absorption term. J. Math. Soc. Japan 53 (2001), no. 3, 513--540. doi:10.2969/jmsj/05330513. https://projecteuclid.org/euclid.jmsj/1213023721