Analysis and Probability Seminar

Abstract: We prove a Weitzenböck identity for general pairs of constant-coefficient homogeneous first-order partial differential operators, and deduce from it sufficient algebraic conditions for coerciveness and Morrey estimates under the natural 1/2 boundary conditions. Our proof of the $W^{1,2}$ elliptic estimate relies on the Aronszajn-Ne{\u c}as-Smith coercive estimate. For generalized strongly pseudoconvex domains, we improve the Morrey estimate to a weighted $W^{1,2}$ square function estimate, using a generalized Cauchy--Pompeiu reproducing formula and the $T1$ theorem for singular integrals. We use Van Schaftingen's notion of cocanceling to study the generalized Levi forms appearing. This is joint work with Erik Duse, FOI.