Removable singularities for quasilinear degenerate elliptic equations with absorption term

Abstract

Let $N\ge 1$ 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 $\Omega \setminus F$ 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.