Speaker:  Klaus Schmitt, University of Utah

Title:  Variational Methods and Quasilinear Elliptic PDEs

Abstract: Let E be a real Banach space and f : E -> R be a C1 functional.
A point u of E is called a critical point of f, if it is the case that
f'(u) is the zero element of the dual space E*. The existence question of
(weak) solutions of many problems in the theory of quasilinear elliptic
(and other) pde's may be solved by finding an appropriate Banach space
E and a C1 functional f : E -> R and establishing the existence
of critical points for f, in other words, the pde problem may be 
formulated in an abstract way as an equation f'(u) = 0,
where f' : E -> E*. In this lecture I shall discuss some
critical point theorems and provide several applications to
quasilinear elliptic partial differential equations. The lecture is
aimed at a general audience and presumes only an entry graduate
level course on real analysis.