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Room P3.10, Mathematics Building
José Francisco Rodrigues, Universidade de Lisboa
The -Membranes Problem for Nonlinear Degenerate Systems
We consider the elliptic variational inequality associated with quasilinear nonlinear systems, including those of -Laplacian type, and with the ordering constraint of the -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 ( ) integrability of second derivatives for all . Considering the -membrane problem as coupled -obstacle problem we obtain also the corresponding conditions for the stability of the coincidence sets for the variation of external forces.