EVENT DETAILS AND ABSTRACT

Title: Strichartz and refined local smoothing estimates for wave equations in strictly concave domains
Speaker: Matthew Blair
Speaker Info: University of New Mexico
Brief Description:
Special Note:
Abstract:

In this talk, we will introduce a family of energy estimates for solutions to the wave and Schrodinger equations in domains with a strictly concave boundary satisfying homogeneous boundary conditions. They can be thought of as refinements of the classical local energy and local smoothing estimates. The estimates show that for frequency localized solutions, taking the square integral of the solution over small frequency-dependent collars of the boundary results in a stronger gain in regularity than would be expected for collars of a uniform size. We will also discuss the consequences for the development of Strichartz estimates with subcritical exponents in such domains, in particular providing an avenue for treating Neumann conditions.