25/01/2024, 14:30, room 1B (RM002)
Diffusion equations in their linearized versions naturally lead to the study of elliptic eigenvalue problems where the eigenvalue appears both in the interior and on the boundary. This kind of spectral problems have surged in the literature only recently and give rise to many appealing questions. In this talk we will review two such problems that showed to be particularly interesting: the first one comes from the Allen-Cahn equation and is associated with the Laplacian, and has already been used to prove interesting results in spectral geometry. The second one comes from the Cahn-Hillard equation and is associated with the bilaplacian. After introducing these two problems, we will recall some basic facts from Spectral Theory and Spectral Geometry to provide context, and then discuss major properties and open problems concerning their eigenvalues.