Seminario EDP UAM-ICMAT
A bridge between convexity and quasiconvexity
Ponente: Julio Rossi (Universidad Torcuato di Tella, Buenos Aires, Argentina)Fecha: viernes 24 de octubre de 2025 - 12:00-13:00Lugar: Aula Naranja, ICMAT
Resumen:
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.
