On a conjecture of J. Serrin

  • Haïm Brezis

    Rutgers University, Piscataway, United States


In 1964 J. Serrin proposed the following conjecture. Let be a weak solution of the second order elliptic equation (1) below, in divergence form, with Hölder continuous coefficients ; then is a “classical” solution. We announce a solution of this conjecture assuming only 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