Sharp estimates for fundamental frequencies of elliptic operators generated by asymmetric seminorms in low dimensions

Abstract

We establish new sharp asymmetric Poincare inequalities in one-dimension with the computation of optimal constants and characterization of extremizers. Using the one-dimensional theory we develop a comprehensive study on fundamental frequencies in the plane and related spectral optimization in the very general setting of positively homogeneous anisotropies.

arXiv comment38 pages, comments are welcome