On removable singular sets for quasilinear elliptic equations

M. V. Tuvaev

Sbornik. Mathematics, Tome 81 (1995) no. 1, pp. 229-234

Résumé

For equations of the form $$ \operatorname{div}(|\nabla u|^{p-2}\nabla u) =\alpha|u|^{\beta_1}|\nabla u|^{\beta_2}\operatorname{sgn}u,\qquad x\in\Omega\subset\mathbb{R}^n, $$ in the case $1$, $\beta_1>0$, $0\leqslant \beta_2\leqslant p$, $\beta_1+\beta_2>p-1$, $\alpha>0$, sufficient conditions are given for removability of singular sets of dimension $\alpha$. These conditions are nearly necessary, and are given by the formula $$ 0\leqslant \alpha \frac{p\beta_1+\beta_2}{\beta_1+\beta_2+1-p}. $$