Surnachev, M. D. On the uniqueness of solutions to stationary convection-diffusion equations with generalized divergence-free drift. (English) Zbl 1388.35029 Complex Var. Elliptic Equ. 63, No. 7-8, 1168-1184 (2018). Summary: Let \(A\) be a skew-symmetric matrix in \(L^2(\Omega)\), \(\Omega\) – a bounded Lipschitz domain in \(\mathbb R^n\), \(n\geq 2\). The Dirichlet problem \(-\operatorname{div}(\nabla u+A\nabla u)=f\), \(u\in W_0^{1,2}(\Omega)\), \(f\in W^{-1,2}(\Omega)\) has at least one solution obtained by approximating \(A\) and passing to the limit. In V. V. Zhikov [Funct. Anal. Appl. 38, No. 3, 173–183 (2004; Zbl 1147.35302); translation from Funkts. Anal. Prilozh. 38, No. 3, 15–28 (2004)] V. V. Zhikov constructed an example of nonuniqueness. In the same paper he proved the uniqueness of solutions if the \(L^p(\Omega)\) norms of \(A\) are \(o(p)\) as \(p\) goes to infinity. We prove the uniqueness of solutions if \(\exp (\gamma| A|)\in L^1(\Omega)\) for some \(\gamma >0\), which generalizes Zhikov’s theorem. 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