ΕΚΔΗΛΩΣΕΙΣ

Ημερομηνία: 15/12/2022

Ώρα: 15:00

Τόπος: Αίθουσα Α32

Ομιλητης: Κωνσταντίνος Γκίκας, ΕΚΠΑ

Τίτλος: Poisson Problems involving fractional Hardy operators and measures

Περίληψη: We study the Poisson problem involving a fractional Hardy operator and a measure source. The complex interplay between the nonlocal nature of the operator, the peculiar effect of the singular potential and the measure source induces several new fundamental difficulties in comparison with the local case. To overcome these difficulties, we perform a careful analysis of the dual operator in the weighted distributional sense and establish fine properties of the associated function spaces, which in turn allow us to formulate the Poisson problem in an appropriate framework. In light of the close connection between the Poisson problem and its dual problem, we are able to establish various aspects of the theory for the Poisson problem including the solvability, a priori estimates, variants of Kato's inequality and regularity results.

Joint work with H. Chen and P.T. Nguyen.

K . G. acknowledges the support by the Hellenic Foundation for Research
and Innovation (H.F.R.I.) under the “2nd Call for H.F.R.I. Research
Projects to support Post-Doctoral Researchers” (Project Number: 59).