Abstract:
Regularity is proved for an arbitrary generalized solution of a quasilinear elliptic equation of divergent type which belongs to Wm+n/22(Ω′), for an arbitrary strictly interior subregion Ω′ of a region Ω (2m is the order of the equation, and n is the number of arguments). It follows from this, in particular, that the regularity problem has an affirmative solution in the two-dimensional case.
Citation:
I. V. Skrypnik, “A regularity condition for generalized solutions of higher-order quasilinear elliptic equations”, Math. USSR-Izv., 7:6 (1973), 1371–1421
\Bibitem{Skr73}
\by I.~V.~Skrypnik
\paper A regularity condition for generalized solutions of higher-order quasilinear elliptic equations
\jour Math. USSR-Izv.
\yr 1973
\vol 7
\issue 6
\pages 1371--1421
\mathnet{http://mi.mathnet.ru/eng/im2365}
\crossref{https://doi.org/10.1070/IM1973v007n06ABEH002090}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1803278}
\zmath{https://zbmath.org/?q=an:0291.35034}
Linking options:
https://www.mathnet.ru/eng/im2365
https://doi.org/10.1070/IM1973v007n06ABEH002090
https://www.mathnet.ru/eng/im/v37/i6/p1376
This publication is cited in the following 3 articles:
Simone Ciani, Eurica Henriques, Igor I. Skrypnik, “On the continuity of solutions to anisotropic elliptic operators in the limiting case”, Bulletin of London Math Soc, 2025
Skrypnik I.I. Voitovych M.V., “on the Generalized U-M,P(F) Classes of de Giorgi-Ladyzhenskaya-Ural'Tseva and Pointwise Estimates of Solutions to High-Order Elliptic Equations Via Wolff Potentials”, J. Differ. Equ., 268:11 (2020), 6778–6820
Mykhailo Voitovych, “Continuity of weak solutions to nonlinear fourth-order equations with strengthened ellipticity via Wolff potentials”, Proc. IAMM NASU, 33 (2019), 33
Citation in format AMSBIB
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