Room P3.10, Mathematics Building

José Francisco Rodrigues, Universidade de Lisboa
The N-Membranes Problem for Nonlinear Degenerate Systems

We consider the elliptic variational inequality associated with quasilinear nonlinear systems, including those of p-Laplacian type, and with the ordering constraint of the N-membrane problem. We extend the Lewy-Stampacchia inequalities for the solution, obtaining new regularity results for the derivatives of the solution, including in the case of linear operators ( p=2) integrability of second derivatives for all q>1. Considering the N-membrane problem as coupled (N-1)-obstacle problem we obtain also the corresponding conditions for the stability of the coincidence sets for the variation of external forces.