This award will support collaborative research between James Serrin, University of Minnesota, and Patrizia Pucci, University of Modena, Italy. The proposed program deals with existence, uniqueness, symmetry, asymptotic and boundary behavior of solutions of linear and quasilinear second order equations or systems of equations of elliptic and parabolic type, and with problems in fluid dynamics. Specific problems to be investigated include the existence and uniqueness of ground state solutions for general equations of variational or non-variational type; behavior of solutions of quasilinear equations or systems of equations of elliptic and parabolic type; properties of fundamental solutions, Harnack inequalities and boundary behavior of solutions of linear elliptic-parabolic equations; symmetry properties of solutions of linear and quasilinear second order equations; and structure of one- dimensional solutions of compressible Navier-Stokes equations. The proposed collaboration will make an important contribution to nonlinear analysis.
