| Abstract: |
| In this talk we consider evolution BVPs for nonlinear fractional operators on irregular domains. It is known that these operators model the so-called anomalous diffusion.\
In particular, we investigate parabolic Robin-Venttsel` problems for regional fractional $p$-Laplace operators on extension domains.
By using nonlinear semigroup theory, we prove that the problems at hand admit unique weak solutions. We then prove regularity properties of the associated nonlinear semigroups, i.e. ultracontractivity properties. This is achieved by means of generalized fractional Green formulas and fractional logarithmic Sobolev inequalities, adapted to the problems at hand.\
We then conclude by mentioning some generalizations and possible future developments.\
These results are obtained in collaboration with M. R. Lancia and P. Vernole. |
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