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

Abstract

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 $(x,y,t)\in {\mathbb{R}}^n\times {\mathbb{R}}^n\times \mathbb{R}$.

References in corpus (1)

• Local behavior of fractional $p$-minimizers