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arXiv · 1803.09562

On maximum and comparison principles for parabolic problems with the $p$-Laplacian

Vladimir Bobkov·Peter Takac
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Abstract

We investigate strong and weak versions of maximum and comparison principles for a class of quasilinear parabolic equations with the $p$-Laplacian $$ \partial_t u - Δ_p u = λ|u|^{p-2} u + f(x,t) $$ under zero boundary and nonnegative initial conditions on a bounded cylindrical domain $Ω\times (0, T)$, $λ\in \mathbb{R}$, and $f \in L^\infty(Ω\times (0, T))$. Several related counterexamples are given.

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Vladimir Bobkov, Peter Takac. 2018-03-26. On maximum and comparison principles for parabolic problems with the $p$-Laplacian. https://doi.org/10.1007/s13398-018-0536-6

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