On a conjecture of J. Serrin

Abstract

sup { vertical-align: 0.8ex; font-size:95%; } sub { vertical-align: -0.8ex; font-size:95%; } .ions { line-height: 1.8; } .ions sub { margin-left: 0.3ex; } .ions sup { vertical-align: 1ex; margin-left: -2.4ex;} In 1964 J. Serrin proposed the following conjecture. Let u ∈ Wloc1,1(Ω) be a weak solution of the second order elliptic equation (1) below, in divergence form, with Hölder continuous coefficients aij(x); then u is a “classical” solution. We announce a solution of this conjecture assuming only u ∈ BVloc(Ω) and Dini continuous coefficients.