On a Conjcture of J. Serrin

GEOMETRIC PDE SEMINAR
Topic:On a Conjcture of J. Serrin
Speaker:Haim Brezis
Affiliation:Rutgers, The State University
Date:Tuesday, February 17
Time/Room:2:00pm - 3:00pm/S-101

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.