On the uniqueness of solutions to stationary convection–diffusion equations with generalized divergence-free drift

Abstract

Let A be a skew-symmetric matrix in , — a bounded Lipschitz domain in , . The Dirichlet problem , , has at least one solution obtained by approximating A and passing to the limit. In 2004 V. V. Zhikov constructed an example of nonuniqueness. In the same paper he proved the uniqueness of solutions if the norms of A are o(p) as p goes to infinity. We prove the uniqueness of solutions if for some , which generalizes Zhikov’s theorem.