Spectral Optimization in Exterior Domains - Robin and Steklov Problems

Explore spectral optimization theory through this 45-minute mathematical seminar examining Robin and Steklov problems in exterior domains. Learn about the classical Steklov problem on bounded domains and its connections to shape optimization, geometric inequalities, and physical applications including diffusion processes with specific boundary behaviors. Discover how extending these concepts to exterior domains leads to the exterior Steklov problem and examine suitable formulations, equivalent characterizations, and limiting approaches for this extension. Analyze classical inequalities such as Weinstock's and derive Escobar-type lower bounds for first eigenvalues, revealing how isoperimetric inequalities fail in exterior settings for higher dimensions even with smooth convex domains. Investigate the exterior Robin problem and understand how similar isoperimetric failures occur for Robin spectra in higher dimensions, building upon results from the Steklov case. Gain insights into collaborative research connecting spectral geometry, mathematical physics, and optimization theory through work involving multiple mathematical institutions and researchers.