Autor: Bernard Dacorogna (Ecole Polytechnique Fédérale Lausanne, Suiça)
Resumo/ementa: In recent years several mathematicians have investigated nonlinear equations, particularly those of second order, both linear and nonlinear and either in divergence or non-divergence form. Quasilinear and fully nonlinear are relevant classes of such equations and have been widely examined. In this short course, we present a (new) family of differential equations called "implicit partial differential equations". We discuss a new functional analytic method based on the Baire category theorem for handling the existence of almost everywhere solutions. The results have been obtained for the most part in important applications to the calculus of variations, nonlinear elasticity, phase transitions and optimal design. We may present some background on viscosity solutions, different notions of convexity, Vitali type covering theorems, and briefly convex integration.
Cronograma: O curso será dividido em 8 aulas, de 13 a 27 de janeiro.
Implicit Partial Differential Equations. (Progress in Nonlinear Differential
Equations and Their Applications), Bernard Dacorogna and Paolo Marcellini.