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.