Abstract:
A Dirichlet problem for a second-order nonlinear elliptic equation in the general divergent form with a right-hand side from L1 is considered. The high-order coefficients in the equation are supposed to satisfy the degenerate coercivity condition. The main results concern a priori properties of summability and some estimates of entropy solutions of this problem.
Citation:
A. A. Kovalevsky, “A priori properties of solutions of nonlinear equations with degenerate coercivity and L1-data”, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 2, CMFD, 16, PFUR, M., 2006, 47–67; Journal of Mathematical Sciences, 149:5 (2008), 1517–1538
\Bibitem{Kov06}
\by A.~A.~Kovalevsky
\paper A priori properties of solutions of nonlinear equations with degenerate coercivity and $L^1$-data
\inbook Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14--21, 2005). Part~2
\serial CMFD
\yr 2006
\vol 16
\pages 47--67
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd48}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2336445}
\transl
\jour Journal of Mathematical Sciences
\yr 2008
\vol 149
\issue 5
\pages 1517--1538
\crossref{https://doi.org/10.1007/s10958-008-0080-6}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84920755446}
Linking options:
https://www.mathnet.ru/eng/cmfd48
https://www.mathnet.ru/eng/cmfd/v16/p47
This publication is cited in the following 5 articles:
L. M. Kozhevnikova, “Entropy and renormalized solutions of anisotropic elliptic equations with variable nonlinearity exponents”, Sb. Math., 210:3 (2019), 417–446
A. A. Kovalevsky, “Integrability Properties of Functions with a Given Behavior of Distribution Functions and Some Applications”, Proc. Steklov Inst. Math. (Suppl.), 308, suppl. 1 (2020), S112–S126
L. M. Kozhevnikova, “Ob entropiinykh resheniyakh anizotropnykh ellipticheskikh uravnenii s peremennymi pokazatelyami nelineinostei v neogranichennykh oblastyakh”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 63, no. 3, Rossiiskii universitet druzhby narodov, M., 2017, 475–493
L. M. Kozhevnikova, “Existence of entropic solutions of elliptic problem in anisotropic Sobolev–Orlicz spaces”, J. Math. Sci. (N. Y.), 241:3 (2019), 258–284
A. A. Kovalevsky, Yu. S. Gorban, “On $T$-solutions of degenerate anisotropic elliptic variational inequalities with $L^1$-data”, Izv. Math., 75:1 (2011), 101–156
Citation in format AMSBIB
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