OPTIMAL L-p HARDY-RELLICH TYPE INEQUALITIES ON THE SPHERE

摘要

In this paper we study some L-p-Hardy-Rellich type inequalities and the corresponding optimal constant on the geodesic sphere. By the divergence theorem, properties of radial Laplacian and geodesic distance, we obtain an improved version of Hardy-Rellich inequalities holding in dimension N >= 3. The result is new for N = 3. 4. Moreover. we show that the constant obtained is optimally sharp.