JournalsrlmVol. 19, No. 4pp. 335–338

On a conjecture of J. Serrin

  • Haïm Brezis

    Rutgers University, Piscataway, United States
On a conjecture of J. Serrin cover
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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.

Cite this article

Haïm Brezis, On a conjecture of J. Serrin. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 19 (2008), no. 4, pp. 335–338

DOI 10.4171/RLM/529