# Research Group on Partial Differential Equations

## Research interests:

Our group is devoted to the analysis of certain partial differential equations and systems appearing in several fields of applications such as combustion theory, fluid mechanics or in general, reaction diffusion processes.

Some of our present interests consist on:

• Nonlinear Elliptic Ecuations with nonstandard growth. We study some nonlinear elliptic equations such as $$p(x)$$-Laplacian type problems or $$\phi$$-Laplacian type problems. In particular we are interested in the regularity properties for solutions, free boundary problems associated to these operators, variational problems with lack of compactness, eigenvalue problems and optimal design problems.
• Homogenization problems. We focus on some homogenization problems for eigenvalues of nonlinear homogeneous operators of $$p$$-Laplace type, in particular we are interested in the order of convergence of these eigenvalues. Also we are interested in homogenization appearing by domain approximations.
• Nonlocal Reaction-diffusion equations. Among the problems under consideration we analyze the asymptotic behavior for reaction-diffusion equations with absorption where the diffusion is given by the fractional laplacian. We also analyze some Stefan-like free boundary problems associated to the fractional laplacian.
• PDE techniques applied to Game Theory. We study some mean fields models where the populations apply different strategies and interact during the game evolving towards some equilibrium states, where the fraction of the players in each strategy corresponds to a Nash equilibrium.
To see a list of publications or to request for a preprint, please check the personal pages of the participants.