University of Connecticut

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Analysis and Probability Seminar
Boundary value problems and Fatou theorems for elliptic systems in the upper half-space
Jose Maria Martell (Institute of Mathematical Sciences, Madrid)

Thursday, April 11, 2019
11:00am – 12:00pm

Storrs Campus
MONT 214

Abstract: In this talk we will consider the Dirichlet problem in the upper half-space for second-order, homogeneous, elliptic systems, with constant complex coefficients, such as the Laplacian or the Lam\'e system of elasticity. The goal is to show that the Dirichlet problem is well-posed with data in Lebesgue spaces (with and without weights), Köte function spaces, BMO, VMO, Hölder spaces, etc. By the work of S. Agmon, A. Douglis, and L. Nirenberg, there exists a Poisson kernel associated with each of the previous operators which can be used to construct solutions in a quite general class of functions containing all the previous spaces. Uniqueness is more delicate and the main idea consists in establishing Fatou type results on which one can recover null solutions from their nontangential boundary traces using the associated Poisson kernel.

Contact:

Scott Zimmerman, scott.zimmerman@uconn.edu

Analysis and Probability Seminar (primary), UConn Master Calendar

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