Nonlinear diffusion and free boundary problems. A conference on the occasion of the 70th anniversary of Juan Luis Vázquez
UAM Madrid (Spain)
May 17-19, 2017
Nonlocal and nonlinear diffusions and interactions
New methods and directions
July 4-8, 2016
Frontiers of Mathematics and Applications IV
July 20-24, 2015
I am a Professor (Contratado Doctor, I3) of the Departamento de Matemáticas at the Universidad Autónoma de Madrid.
I am PI2 of the Spanish research group MTM2014-52240-P, "Ecuaciones de Difusión No Lineales y Aplicaciones" - "Nonlinear Diffusion Equations and Applications" - PI1 Juan Luis Vázquez and founded by MINECO (Spanish Government).
I am member of the editorial board of the Journal Nonlinear Analysis.
In this academic year 2016/2017 I am teaching two courses at UAM: Partial Differential Equations for students of the Master in Mathematics and Calculus I for students of the 1st year of Engineering (Informatics).
Nonlinear and/or nonlocal partial differential equations:
asymptotic properties, rates of convergence to equilibrium, regularity and Harnack inequalities for degenerate and singular nonlinear -and also nonlocal- parabolic PDE in the Euclidean setting and on Riemannian manifolds. Nonlinear (fast) diffusion flows of porous medium or p-Laplacian type. Total variation flow.
Functional inequalities (also with weights): Sobolev, Gagliardo-Nirenberg, Hardy, Poincaré, Logarithmic Sobolev, [...] and their application to PDE.
Entropy methods for nonlinear flows, in the Euclidean setting and on Riemannian manifolds: a bridge from functional inequalities to PDE and geometry.