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Title: Spectral Optimization for the Robin Laplacian in Exterior Domains

Abstract:听The spectrum of the Laplace operator with Robin boundary conditions on bounded domains is a well-studied area with important physical applications. For example, in analyzing the long-term behavior of Brownian motion with particle creation at the boundary, the principal eigenvalue provides information about the expected number of particles within the domain.

When the domain is unbounded鈥攕pecifically, the complement of a compact set鈥攏ew questions and challenges emerge, holding potential relevance in quantum theory.

In this talk, I will discuss the existence of discrete eigenvalues s well as the problem of geometrically optimizing the lowest point of the spectrum. We will see that, while the ball serves as a local maximizer among domains of fixed measure, it does not necessarily achieve the global optimum.

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Meeting ID: 895 2873 0384

Passcode: 077937

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