http://orcid.org/0000-0003-4071-5097
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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.
Acknowledgements
The author thanks the unanimous referee whose remarks helped to improve this paper.
Notes
No potential conflict of interest was reported by the authors.
Dedicated to the memory of Academician V. I. Smirnov, One of the Founding Fathers of MathPhys in Russia.
Additional information
Funding
The work was partially supported by the Russian Foundation for Basic Research, [project number 15-01-00471], and by the Ministry of Education and Science of the Russian Federation, [research project number 1.3270.2017/4.6].