Special Session 35: Elliptic PDEs: singularities, discontinuities, and nonlinear phenomena

1-Laplace Dirichlet problems involving first order terms
Francescantonio Oliva
Sapienza university of Rome
Italy
Co-Author(s):    
Abstract:
In this talk, we discuss the existence and qualitative behavior of bounded variation (BV) solutions to Dirichlet problems driven by the 1-Laplace operator. We deal with general, and possibly singular, first-order nonlinearities and we focus on how these nonlinearities play a regularizing effect on the solutions. In particular, we study the role of the gradient nonlinearity in the attainment of the homogeneous boundary condition for the solutions.