The L^p-ellipticity and L^p-Dirichlet problems of second order elliptic systems

Abstract: In this talk we will discuss a structural condition of second order elliptic systems with complex coefficients, namely the L^p-ellipticity condition, which can be viewed as an L^p version of the classical ellipticity condition. Such condition naturally implies both interior and boundary estimates, which act as a proper substitution of the De Giorgi-Nash-Moser regularity theory. The new regularity result will help us to prove an extrapolation theorem of the L^p-Dirichlet problem and we will apply it to two well-studied cases: Lam\'e equations and homogenization problems. This is a joint work with M. Dindos and J. Pipher.

analysis of PDEsclassical analysis and ODEs

Audience: researchers in the topic

HA-GMT-PDE Seminar

Series comments: Description: A senior graduate student/postdoc series in harmonic analysis, geometric measure theory, and partial differential equations.

Meetings will be weekly, and usually will occur on Monday, with some exceptions. For each talk, the Zoom link is made available in the website too. Contact Bruno Poggi at poggi008@umn.edu if you would like to subscribe to the seminar mailing list.