Introduction to Non-Linear problems, the Obstacle Problem: part I

18 Maio 2017, 11:00 • Hugo Tavares

Introduction to the obstacle problem as an elastic and a geometrical equilibrium problems; the variational inequality formulation and the interpretation as a free boundary problem. The well-posedness of variational solutions as the projection over a convex set in the Sobolev space H^1_o in the case of linear elliptic operators of second order with Dirichlet boundary condition. Extension to the non symmetric linear and monotone operators — the Lions-Stampacchia theorem. The case of the minimal surfaces quasilinear operator and the need of a priori estimates on the gradient.