Geometric PDE Seminar

In 1964 J. Serrin proposed the following conjecture. Let u be a weak solution (in W^{1,1}) of a second order elliptic equation in divergence form, with Holder continuous coefficients, then u is a "classical" solution ( i.e. u belongs to H^1). I will present a solution to this conjecture assuming even weaker conditions on u (e.g. u in BV ) and on the coefficients. Some intriguing questions remain open if the coefficients are just continuous.