Programa “PUENTES MATEMÁTICOS CON LATINOAMÉRICA” 2025
Seminario de EDP

Conferenciante: Julio D. Rossi
Lugar: ICMAT, sala Naranja

Viernes 24 de octubre, 12:00-13:00: 

Title: A bridge between convexity and quasiconvexity

Abstract: We introduce a notion of convexity with respect to a one-dimensional operator and with this notion find a one-parameter family of different convexities that interpolates between classical convexity and quasiconvexity. We show that, for this interpolation family, the convex envelope of a continuous boundary datum in a strictly convex domain is continuous up to the boundary and is characterized as being the unique viscosity solution to the Dirichlet problem in the domain for a certain fully nonlinear partial differential equation that involves the associated operator. In addition we prove that the convex envelopes of a boundary datum constitute a one-parameter curve of functions that goes from the quasiconvex envelope to the convex envelope being continuous with respect to uniform convergence.

Joint work with P. Blanc and M. Parviainen.