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arXiv · 1409.8479

A generalized porous medium equation related to some singular quasilinear problems

Francesco Petitta
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Abstract

In this paper we study existence and nonexistence of solutions for a Dirichlet boundary value problem whose model is $$ \begin{cases} -\sum_{m=1}^{\infty} a_m Δu^m= f&\text{in}\ Ω\newline u=0 & \text{on}\ \partialΩ\,, \end{cases} $$ where $Ω$ is a bounded domain of $\mathbb{R}^N$, $a_m$ is a sequence of nonnegative real numbers, and $f$ is in $L^q(Ω)$, $q>\frac{N}{2}$.

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Francesco Petitta. 2014-09-30. A generalized porous medium equation related to some singular quasilinear problems. https://arxiv.org/abs/1409.8479

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