1:00 pm Wednesday, April 26, 2023
Analysis Seminar: Integro-differential equations in Orlicz-Sobolev spaces: some recent results and open problems by Hernan Vivas (University of Mar del Plata) in PMA 10.176
Orlicz-Sobolev spaces are the natural setting for the study of variational problems with nonstandard growth, meaning that the energy under consideration is given by a potential whose behavior is different from a power. Such problems are typical, for instance, of statistical physics, where the exponential and entropic functions play a crucial role. Integro-differential equations, on the other hand, appear in the study of Levy processes with jumps in which the infinitesimal generator of a stable pure jump process is given, through the Levy-Khintchine formula, by an integro-differential operator. These have proven to be accurate models to describe phenomena in physics, biology, meteorology, and finance among many other fields. In this talk we will discuss some recent results for integro-differential equations posed in fractional Orlicz-Sobolev spaces, ranging from eigenvalue problems to regularity and qualitative issues, and present some open problems and questions which we consider of interest. These are joint works with Julian Fernandez Bonder and Ariel Salort. Submitted by
|
|