Abstract:
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 $1<p<n$, $\beta_1>0$, $0\leqslant \beta_2\leqslant p$, $\beta_1+\beta_2>p-1$,
$\alpha>0$, sufficient conditions are given for removability of singular sets of dimension
$\alpha$. These conditions are nearly necessary, and are given by the formula
$$
0\leqslant \alpha <n-\frac{p\beta_1+\beta_2}{\beta_1+\beta_2+1-p}.
$$
Fulltext:
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