Πέμπτη 13 Φεβρουαρίου, Αίθουσα Μ2, 11.15-12.00.
Ομιλητής: Κωνσταντίνος Τζιράκης, ΑΠΘ
Τίτλος: Sharp weighted Finsler-Kato inequalities for anisotropic Laplacian
Περίληψη: The talk concerns recent developments in anisotropic weighted Kato type inequalities – with the anisotropy being represented by a generic Finsler metric – which are associated to the so-called Finsler or anisotropic Laplacian. The Finsler Laplacian is one of the most natural and foremost operators in the theory of anisotropic and non homogeneous media (also in Finsler or Minkowski geometry).
Following a unifying approach, we establish first a sharp interpolation between anisotropic weighted Hardy and Kato inequalities, in the half-space, extending the corresponding non-weighted version, being established recently by a different approach. Then, passing to bounded domains, we obtain successive sharp improvements by adding correction terms involving sharp weights and optimal constants, resulting in an infinite series-type improvement.
The specific weight being involved is motivated by applications, via local-type PDEs approach, to non-local Fractional Laplacians; we discuss this approach. We also discuss the optimality of the weights and the constants of the remainder terms, and time permitting, the results within the special Euclidean context, as well as the application of our method for cones.