Failure of the Hopf-Oleinik lemma for a linear elliptic problem with singular convection of non-negative divergence

Lucio Boccardo, David Gómez-Castro, Jesús Ildefonso Díaz

In this paper we study existence, uniqueness, and integrability of solutions to the Dirichlet problem $-\mathrm{div}(M(x)\nabla u)=-\mathrm{div}(E(x)u)+f$ in a bounded dom…