Finsler-Rellich inequalities involving the distance to the boundary

Abstract

We study Rellich inequalities associated to higher-order elliptic operators in the Euclidean space. The inequalities are expressed in terms of an associated Finsler metric. In the case of half-spaces we obtain the sharp constant while for a general convex domain we obtain estimates that are better than those obtained by comparison with the polyharmonic operator.

8 pages, 2 figures; minor changes; to appear in the Proc. Amer. Math. Soc