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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2002, Volume 236, Pages 318–327 (Mi tm301)  
On the Uniqueness Problem for Nonlinear Elliptic and Parabolic Equations

I. V. Skrypnika, G. Gaevsib

a Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences
b Weierstrass-Institut für Angewandte Analysis und Stochastik
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Abstract: The Dirichlet and the Cauchy–Dirichlet problems for second-order nonlinear elliptic and parabolic equations are studied in the case of strongly growing or degenerate leading coefficients. The solvability of the problems and the uniqueness of their solutions are proved, energy estimates and estimates for the maximum of the solutions are established.
Received in February 2001
Bibliographic databases:
UDC: 517.9
Language: Russian
Citation: I. V. Skrypnik, G. Gaevsi, “On the Uniqueness Problem for Nonlinear Elliptic and Parabolic Equations”, Differential equations and dynamical systems, Collected papers. Dedicated to the 80th anniversary of academician Evgenii Frolovich Mishchenko, Trudy Mat. Inst. Steklova, 236, Nauka, MAIK «Nauka/Inteperiodika», M., 2002, 318–327; Proc. Steklov Inst. Math., 236 (2002), 305–314
Citation in format AMSBIB
\Bibitem{SkrGae02}
\by I.~V.~Skrypnik, G.~Gaevsi
\paper On the Uniqueness Problem for Nonlinear Elliptic and Parabolic Equations
\inbook Differential equations and dynamical systems
\bookinfo Collected papers. Dedicated to the 80th anniversary of academician Evgenii Frolovich Mishchenko
\serial Trudy Mat. Inst. Steklova
\yr 2002
\vol 236
\pages 318--327
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm301}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1931031}
\zmath{https://zbmath.org/?q=an:1125.35354}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2002
\vol 236
\pages 305--314
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