A nonlocal isoperimetric problem: density perimeter

Speaker: Andrés Zúñiga

Universidad de O’Higgins

Date: July 6, 2022 at 12 Santiago time

Abstract: We will discuss a variant of a classical geometric minimization problem, known as the “nonlocal isoperimetric problem”, which arises from studies in Nuclear Physics by Gamow in the 1930’s. By introducing a density in the perimeter functional, we obtain features that differ substantially from existing results in the framework of the classical problem without densities. In the regime of “small” non-local contribution, we completely characterize the minimizer, in the case the density is a monomial radial weight. This work is a collaboration with Stan Alama and Lia Bronsard (McMaster University) and Ihsan Topaloglu (Virginia Commonwealth University), as part of the project QUALITATIVE PROPERTIES OF WEIGHTED AND ANISOTROPIC VARIATIONAL PROBLEMS financed by ANID CHILE FONDECYT INICIACION Nº 11201259.

Venue: Online via Zoom / Sala de seminarios DIM, Beauchef 851, piso 5
Chair: Claudio Muñoz