The Dirichlet problem for possibly singular elliptic equations with degenerate coercivity

Abstract

We deal with existence, uniqueness and regularity of nonnegative solutions to a Dirichlet problem for equations as \begin{equation*} \displaystyle -\operatorname{div}\left(\frac{|\nabla u|^{p-2}\nabla u}{(1+u)^{θ(p-1)}}\right) = h(u)f \quad \text{in }Ω, \end{equation*} where $\Omega$ is an open bounded subset of ${\mathbb{R}}^N$ ($N\ge 2$), $p>1$, $\theta \ge 0$, $f\ge 0$ belongs to a suitable Lebesgue space and $h$ is a continuous, nonnegative function which may blow up at zero and it is bounded at infinity.

37 pages

References in corpus (1)

• Spreading equilibria under mildly singular potentials: pancakes versus droplets