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

2025/01/22 by Julián Haddad, Haddad, Julian, Raul Fernandes Horta +3
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2501.12939

openalex publication_date 2025/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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