Convergence of fractional diffusion processes in extension domains
We study the asymptotic behavior of anomalous fractional diffusion processes in bad domains via
the convergence of the associated energy forms.We introduce the associated Robin–Venttsel’ problems for
the regional fractional Laplacian. We provide a suitable notion of fractional normal derivative on irregular
sets via a fractional Green formula as well as existence and uniqueness results for the solution of the
Robin–Venttsel’ problem by a semigroup approach. Submarkovianity and ultracontractivity properties of
the associated semigroup are proved.