Dr. Alejandro Vélez Santiago
Departamento de Ciencias Matemáticas

 

“A class of nonlinear boundary value problems on general domains”

 

The main goal of this research proposal is to investigate the solvability and global regularity theory for a general class of nonlinear elliptic problems with various boundary conditions, on a wide class of domains which include non-smooth and fractal domains.  The two main branches consist of the following: first, existence, nonexistence, multiplicity, and global regularity theory for nonlinear boundary value problems when the exponent is constant, and secondly, the solvability and global regularity theory for nonlinear differential equations with variable exponents on various domains.