MATH Seminar

Title: Regularity estimates for elliptic transmission problems
Seminar: Analysis and Differential Geometry
Speaker: Pablo Raúl Stinga of Iowa State University
Contact: Maja Taskovic, maja.taskovic@emory.edu
Date: 2023-10-13 at 2:00PM
Venue: MSC W301
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Abstract: We present regularity estimates for solutions to transmission problems driven by second order elliptic equations with curved interfaces. First, we consider a transmission problem for harmonic functions and use the mean value theorem to prove sharp $C^{1,\alpha}$ estimates up to the transmission surface. Then, we show various up to the boundary Hölder regularity estimates for viscosity solutions to transmission problems for fully nonlinear uniformly elliptic equations depending on the regularity of the interface. Among the main tools, we introduce an ABP estimate for the problem and new constructive stability results. These are joint works with Luis A. Caffarelli (UT Austin) and María Soria-Carro (Rutgers)