University of Connecticut

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Analysis and Probability Seminar
Regularity of Solutions for Elliptic System With Complex Coefficients
Jungang Li (Brown University)

Friday, May 1, 2020
1:30pm – 2:30pm

Storrs Campus
Webex

Abstract: In the past decades, L^p-Dirichlet problems have been extensively studied under various conditions towards the coefficients and boundary. Nevertheless, much fewer is known for elliptic equations with complex coefficients. This is due to the lack of maximum principles and the De Giorgi-Nash-Moser theory. More recently, Dindos and Pipher introduced a p-ellipticity condition, which enables one to obtain regularity results for solutions, and hence establish the solvability of the L^p-Dirichlet problem in the complex setting. In this talk, we will discuss the generalization of such condition to elliptic systems with complex coefficients. WIth the help of such condition, we obtain the solvability of the L^p-Dirichlet problem together with an extrapolation theory. As application, we consider the Lam\'e system and obtain a wider range of L^p solvability. This is a joint work with Dindos and Pipher.

Contact:

sean.li@uconn.edu

Analysis and Probability Seminar (primary), UConn Master Calendar

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