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Zap. Nauchn. Sem. POMI, 2013, Volume 410, Pages 168–186 (Mi znsl5628)  

This article is cited in 5 scientific papers (total in 5 papers)

On the regularity of solutions to the equation $-\Delta u+b\cdot\nabla u=0$

N. Filonovab

a St. Petersburg Department of Steklov Mathematical Institute, 27 Fontanka, 191023 St. Petersburg
b St. Petersburg State University, Physics Faculty

Abstract: The equation $-\Delta u+b\cdot\nabla u=0$ is considered. The dependence of the local regularity of a solution $u$ on the properties of the coefficient $b$ is investigated.

Key words and phrases: elliptic equations, regularity of solutions.

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English version:
Journal of Mathematical Sciences (New York), 2013, 195:1, 98–108

Bibliographic databases:

UDC: 517
Received: 18.12.2012
Language:

Citation: N. Filonov, “On the regularity of solutions to the equation $-\Delta u+b\cdot\nabla u=0$”, Boundary-value problems of mathematical physics and related problems of function theory. Part 43, Zap. Nauchn. Sem. POMI, 410, POMI, St. Petersburg, 2013, 168–186; J. Math. Sci. (N. Y.), 195:1 (2013), 98–108

Citation in format AMSBIB
\Bibitem{Fil13}
\by N.~Filonov
\paper On the regularity of solutions to the equation $-\Delta u+b\cdot\nabla u=0$
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~43
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 410
\pages 168--186
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5628}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3048265}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 195
\issue 1
\pages 98--108
\crossref{https://doi.org/10.1007/s10958-013-1566-4}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84898970898}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. D. Surnachev, “O edinstvennosti reshenii zadachi o statsionarnoi diffuzii v neszhimaemom turbulentnom potoke”, Preprinty IPM im. M. V. Keldysha, 2015, 096, 32 pp.  mathnet
    2. Kim H., Kim Y.-H., “on Weak Solutions of Elliptic Equations With Singular Drifts”, SIAM J. Math. Anal., 47:2 (2015), 1271–1290  crossref  mathscinet  zmath  isi  scopus
    3. Hara T., “Weak-Type Estimates and Potential Estimates For Elliptic Equations With Drift Terms”, Potential Anal., 44:1 (2016), 189–214  crossref  mathscinet  zmath  isi  elib  scopus
    4. N. Q. Le, “On optimal Hölder regularity of solutions to the equation $\Delta u+b\cdot\nabla u=0$ in two dimensions”, C. R. Math. Acad. Sci. Paris, 355:4 (2017), 439–446  crossref  mathscinet  zmath  isi  scopus
    5. M. D. Surnachev, “On the uniqueness of solutions to stationary convection-diffusion equations with generalized divergence-free drift”, Complex Var. Elliptic Equ., 63:7-8, SI (2018), 1168–1184  crossref  mathscinet  zmath  isi  scopus
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