Nonlinear Analysis of PDE
The Nonlinear Analysis is one of the areas of Mathematics that has presented greater growth in the last years due to the fact that the methods developed there are adaptable to many others areas of Mathematics and to different types of Partial Differential Equations. These methods constitute a powerful tool to understand and to solve diverse problems coming from models in Biology, Finance and Control Theory.
Our group has special interest in studying fully nonlinear local and nonlocal elliptic and parabolic equations, which does not prevent us from dealing with problems that involve only the Laplace operator.
We are interested in proving existence and obtaining qualitative properties of the solutions for these types of equations. We have also a special interest in understanding the complexity of the solution sets that these equations sometimes hide. Notice that most of the qualitative properties and the structure of the solution sets that we are searching for will give rise to different interpretations from the theoretical and the applied point of views.