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Title: Behavior of Absorbing and Generating p-Robin Eigenvalues in Bounded and Exterior Domains

Abstract:听The spectrum of the Laplace operator with Robin boundary conditions has been studied extensively, with deep connections to physical models including heat flow, fluid dynamics, and wave propagation. Its nonlinear counterpart, the p-Laplacian, also plays a central role in modeling complex media, particularly non-Newtonian fluids.

In this talk, we investigate the principal eigenvalue of the p-Laplacian under Robin boundary conditions, with a focus on its asymptotic behavior depending on the boundary parameter. For bounded domains, we establish quantitative inequalities valid for all p, which in particular improve known results in the classical case (p=2). In the setting of exterior domains, we address questions of existence, derive general bounds for the first eigenvalue of the complement of a ball, and prove sharp geometric inequalities for the complement of convex domains in two dimensions.

Title: Behavior of Absorbing and Generating p-Robin Eigenvalues in Bounded and Exterior Domains

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Abstract: The spectrum of the Laplace operator with Robin boundary conditions has been studied extensively, with deep connections to physical models including heat flow, fluid dynamics, and wave propagation. Its nonlinear counterpart, the p-Laplacian, also plays a central role in modeling complex media, particularly non-Newtonian fluids.

In this talk, we investigate the principal eigenvalue of the p-Laplacian under Robin boundary conditions, with a focus on its asymptotic behavior depending on the boundary parameter. For bounded domains, we establish quantitative inequalities valid for all p, which in particular improve known results in the classical case (p=2). In the setting of exterior domains, we address questions of existence, derive general bounds for the first eigenvalue of the complement of a ball, and prove sharp geometric inequalities for the complement of convex domains in two dimensions.

Where: UdeM, Pavillon Andr茅-Aisentstadt, room 5183, or via Zoom (see below)

Join Zoom Meeting

Meeting ID: 895 2873 0384

Passcode: 077937

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