A Faber–Krahn inequality for the Riesz potential operator for triangles and quadrilaterals
Rajesh Mahadevan
Universidad de Concepción, ChileFranco Olivares-Contador
Universidad de Concepción, Chile
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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.
Cite this article
Rajesh Mahadevan, Franco Olivares-Contador, A Faber–Krahn inequality for the Riesz potential operator for triangles and quadrilaterals. J. Spectr. Theory 11 (2021), no. 4, pp. 1935–1951
DOI 10.4171/JST/390