Nonlocal heat equations: decay estimates and Nash inequalities

Cristina Brändle, Arturo de Pablo

We obtain $L^q$--$L^p$ decay estimates, $1\le q<p<\infty$ for solutions of nonlocal heat equations of the form ${\partial }_{t}u+\mathcal{L}u=0$. Here $\mathcal{L}$ is an integral oper…