Local boundedness of solutions to nonlocal equations modeled on the fractional p-Laplacian

11 Dec 2017  ·  Strömqvist Martin ·

We state and prove estimates for the local boundedness of subsolutions of non-local, possibly degenerate, parabolic integro-differential equations of the form \begin{equation*} \partial_tu(x,t)+\mbox{P.V. }\int\limits_{\mathbb R^n}K(x,y,t) |u(x,t)-u(y,t) |^{p-2}(u(x,t)-u(y,t))\, dy,\end{equation*} $(x,t)\in\mathbb R^n\times\mathbb R$, where $\mbox{P.V.}.. $ means in the principle value sense, $p\in (1,\infty)$ and the kernel obeys $K(x,y,t)\approx |x-y |^{n+ps}$ for some $s\in (0,1)$, uniformly in $(x,y,t)\in\mathbb R^n\times \mathbb R^n\times\mathbb R$. read more

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Analysis of PDEs