Nonlocal problems

A great variety of phenomena in Mathematical Physics and Engineering have an intrinsic nonlocal nature. In the last decade, there has been a growing interest in taking nonlocal nature into consideration in mathematical models, leading to the mathematical analysis of wide variety of nonlocal and fractional models.

We are particularly interested in nonlocal variational problems, considering questions from existence conditions to the study of relaxation when problems lack optimal solutions. From a more applied point of view, our main interest is to include nonlocal modeling into the mathematical theory of hyperelasticity, with the motivation of including typical singular situations when materials deform a lot as fracture, cavitation of multiscale phenomena in general.