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arXiv · 1407.3602

Regularity of the extremal solution for singular p-Laplace equations

Daniele Castorina
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Abstract

We study the regularity of the extremal solution $u^*$ to the singular reaction-diffusion problem $-\Delta_p u = \lambda f(u)$ in $\Omega$, $u =0$ on $\partial \Omega$, where $1 p+2$ and $|\nabla u^*|^{p-1} \in L^{\frac{n}{n-(p'+1)}} (\Omega)$ if $n > p p'$.

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Daniele Castorina. 2014-07-14. Regularity of the extremal solution for singular p-Laplace equations. https://doi.org/10.1007/s00229-014-0711-9

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