V. V. Zhikov, “To the Problem of Passage to the Limit in Divergent Nonuniformly Elliptic Equations”, Funktsional. Anal. i Prilozhen., 35:1 (2001), 23–39; Funct. Anal. Appl., 35:1 (2001), 19

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Funktsional'nyi Analiz i ego Prilozheniya, 2001, Volume 35, Issue 1, Pages 23–39
DOI: https://doi.org/10.4213/faa229 (Mi faa229)

This article is cited in 27 scientific papers (total in 27 papers)

To the Problem of Passage to the Limit in Divergent Nonuniformly Elliptic Equations

V. V. Zhikov

Vladimir State Pedagogical University

Full-text PDF (208 kB) Citations (27)

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DOI: https://doi.org/10.4213/faa229

Abstract: A weighted Sobolev space is constructed in which smooth functions are not dense and their closure is of codimension one. With the help of this weighted space, counterexamples are constructed to natural hypotheses on the passage to the limit in non-uniformly-elliptic equations and on the structure of the limit equation.

Received: 27.08.1999

English version:
Functional Analysis and Its Applications, 2001, Volume 35, Issue 1, Pages 19–33
DOI: https://doi.org/10.1023/A:1004168415999

Bibliographic databases:

Document Type: Article

UDC: 517.9

Language: Russian

Citation: V. V. Zhikov, “To the Problem of Passage to the Limit in Divergent Nonuniformly Elliptic Equations”, Funktsional. Anal. i Prilozhen., 35:1 (2001), 23–39; Funct. Anal. Appl., 35:1 (2001), 19–33

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https://doi.org/10.4213/faa229

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This publication is cited in the following 27 articles:

Nicolas Clozeau, Antoine Gloria, “Quantitative Nonlinear Homogenization: Control of Oscillations”, Arch Rational Mech Anal, 247:4 (2023)
L. S. Efremova, V. Zh. Sakbaev, “Notion of blowup of the solution set of differential equations and averaging of random semigroups”, Theoret. and Math. Phys., 185:2 (2015), 1582–1598
Bankevich S.V., Nazarov A.I., “on Monotonicity of Some Functionals Under Rearrangements”, Calc. Var. Partial Differ. Equ., 53:3-4 (2015), 627–647
Cardone G., Pastukhova S.E., Perugia C., “Estimates in Homogenization of Degenerate Elliptic Equations by Spectral Method”, Asymptotic Anal., 81:3-4 (2013), 189–209
V. Zh. Sakbaev, “Gradient blow-up of solutions to the Cauchy problem for the Schrödinger equation”, Proc. Steklov Inst. Math., 283 (2013), 165–180
V. Zh. Sakbaev, “Cauchy problem for degenerating linear differential equations and averaging of approximating regularizations”, Journal of Mathematical Sciences, 213:3 (2016), 287–459
Dzh. O. Ogun, Yu. N. Orlov, V. Zh. Sakbaev, “O preobrazovanii prostranstva nachalnykh dannykh dlya zadachi Koshi s osobennostyami resheniya tipa vzryva”, Preprinty IPM im. M. V. Keldysha, 2012, 087, 31 pp.
V. Zh. Sakbaev, “On the properties of ambiguity and irreversibility of dynamical maps of the initial data space of Cauchy problem”, P-Adic Num Ultrametr Anal Appl, 4:4 (2012), 306
V. V. Zhikov, S. E. Pastukhova, “Lemmas on compensated compactness in elliptic and parabolic equations”, Proc. Steklov Inst. Math., 270 (2010), 104–131
Sakbaev V.Zh., “Stochastic Properties of Degenerated Quantum Systems”, Infin Dimens Anal Quantum Probab Relat Top, 13:1 (2010), 65–85
V. V. Zhikov, “On the Technique for Passing to the Limit in Nonlinear Elliptic Equations”, Funct. Anal. Appl., 43:2 (2009), 96–112
V. V. Zhikov, S. E. Pastukhova, “Homogenization of degenerate elliptic equations”, Siberian Math. J., 49:1 (2008), 80–101
V. Zh. Sakbaev, “Spectral Aspects of Regularization of the Cauchy Problem for a Degenerate Equation”, Proc. Steklov Inst. Math., 261 (2008), 253–261
Sakbaev, VZ, “Approximation and variational methods for regularization of ill-posed problems”, Doklady Mathematics, 77:2 (2008), 208
Kolesnikov, AV, “Weak convergence of diffusion processes on Wiener space”, Probability Theory and Related Fields, 140:1–2 (2008), 1
S. E. Pastukhova, “Degenerate equations of monotone type: Lavrent'ev phenomenon and attainability problems”, Sb. Math., 198:10 (2007), 1465–1494
Zhikov, VV, “Nash-Aronson estimates for solutions to some parabolic equations: Application to asymptotic diffusion problems”, Doklady Mathematics, 75:2 (2007), 247
Dreyfuss, P, “Higher integrability of the gradient in degenerate elliptic equations”, Potential Analysis, 26:2 (2007), 101
V. G. Sakbaev, “Degeneration and regularization of the operator in the Cauchy problem for the Schrödinger equation”, J Math Sci, 147:1 (2007), 6483
V. Zh. Sakbaev, “On the dynamics of quantum states generated by the Cauchy problem for the Schrödinger equation with degeneration on the half-line”, J. Math. Sci., 151:1 (2008), 2741–2753

Citing articles in Google Scholar: Russian citations, English citations
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