Prof. Maria Rosaria Lancia “Non autonomous fractional equations in extension domains: results and open problems”

In this talk, I will explore non-autonomous fractional (in space and time) semilinear equations with Venttsel-type boundary conditions in irregular domains, potentially with fractal boundaries. The focus will be on well-posedness and regularity results for the mild solutions of the corresponding semilinear Cauchy problem, via the evolution family U(t, s).
I will also present results on the ultracontractivity properties of the evolution family and discuss some recent open problems in the field.