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arXiv · 1907.13027

Boundedness of stable solutions to nonlinear equations involving the $p$-Laplacian

Pietro Miraglio
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Abstract

We consider stable solutions to the equation $ -\Delta_p u =f(u) $ in a smooth bounded domain $\Omega\subset\mathbb{R}^n $ for a $ C^1 $ nonlinearity $f$. Either in the radial case, or for some model nonlinearities $f$ in a general domain, stable solutions are known to be bounded in the optimal dimension range $n 2$.

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Pietro Miraglio. 2019-07-30. Boundedness of stable solutions to nonlinear equations involving the $p$-Laplacian. https://doi.org/10.1016/j.jmaa.2020.124122

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