Anton Selitsky will lecture on “Fractional Powers of Operators Corresponding to Coercive Problems in Lipschitz Domains” on Wednesday, March 4 at 3:00 pm in TUC 244.
Abstract: In this talk, a second-order strongly elliptic (matrix) operator L will be discoursed in a bounded Lipschitz domain Q (n>1). We will study the problem Lu=f with homogeneous boundary conditions (Dirichlet, Neumann, or mixed). Our consideration allows us to prove the Kato problem about the domain of the square root of the operator (1961) in a very simple way. It was solved in 2001 by A. McIntosh and others for bounded measurable coefficients, but our method allows us to consider operator coefficients bounded in the Sobolev spaces with a small smoothness exponent as well, and also Dirichlet-to-Neuman problems. The main approach is based on the Shneiberg theorem about extrapolation of the invertibility of a bounded operator in the interpolation scale. The results can be used for the description of the space of the initial data for corresponding parabolic problems.
This is joint work with Mikhail Agranovich.
The Geometry and Geometric Analysis (GAGA) Seminar is an opportunity for geometers, topologists, and others from TCU and UT Arlington to learn about new topics of mutual interest.
We keep an archive of notes from past GAGA lectures.