Coerciveness and Morrey inequalities for elliptic operators with natural boundary conditions via Weitzenböck identities

Journal article, 2026

We prove a Weitzenb & ouml;ck 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} $ W1,2 elliptic estimate relies on the Aronszajn-Ne $ \breve{c} $ cas-Smith coercive estimate. For generalized strongly pseudoconvex domains, we improve the Morrey estimate to a weighted $ W{1,2} $ W1,2 square function estimate, using a generalized Cauchy-Pompeiu reproducing formula and the $ T1 $ T1 theorem for singular integrals. We use Van Schaftingen's notion of cocanceling to study the generalized Levi forms appearing.