Published

Equations aux dérivées partielles

Refined Rellich boundary inequalities for the derivatives of a harmonic function

Published on

Authors: Siddhant Agrawal, Thomas Alazard

See the publication on HAL

The classical Rellich inequalities imply that the L 2-norms of the normal and tangential derivatives of a harmonic function are equivalent. In this note, we prove several refined inequalities, which make sense even if the domain is not Lipschitz. For two-dimensional domains, we obtain a sharp L p-estimate for 1 < p ≤ 2 by using a Riemann mapping and interpolation argument.