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.