A Faber–Krahn inequality for the Riesz potential operator for triangles and quadrilaterals

Abstract

We prove an analog of the Faber–Krahn inequality for the Riesz potential operator. The proof is based on Riesz’s inequality under Steiner symmetrization and the continuity of the first eigenvalue of the Riesz potential operator with respect to the convergence, in the complementary Hausdorff distance, of a family of uniformly bounded non-empty convex open sets.