Speaker
Delia Schiera, Instituto Superior Técnico, Lisboa
Abstract
We consider a family of pure Neumann \(p\)-Laplacian problems, including eigenvalue problems. Using variational methods, we develop a unified framework that establishes existence of solutions and characterizes their asymptotic behavior as the parameters vary. This approach reveals a natural asymptotic connection between pure Neumann \(p\)-Laplacian equations and a relative isoperimetric problem known as the Neumann-Cheeger problem. We describe the shape of minimizers in domains with different geometries and obtain results on regularity, uniqueness, multiplicity, symmetry, and symmetry breaking phenomena.
Joint work with S. McCurdy and A. Saldaña.