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 Mat. Sb. (N.S.), 1986, Volume 131(173), Number 4(12), Pages 477–500 (Mi msb1974)

The first boundary value problem for nondivergence second order parabolic equations with discontinuous coefficients

Yu. A. Alkhutov, I. T. Mamedov

Abstract: This paper is concerned with the questions of solvability and smoothness of weak solutions of the first boundary value problem for a parabolic equation of the form
$$\mathscr Lu=\sum^n_{i,k=1}a_{ik}(t,x)u_{x_ix_k}-u_t=f(t,x).$$

Bibliography: 18 titles.

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English version:
Mathematics of the USSR-Sbornik, 1988, 59:2, 471–495

Bibliographic databases:

UDC: 517.956.4
MSC: Primary 35K20; Secondary 35B65, 35R05

Citation: Yu. A. Alkhutov, I. T. Mamedov, “The first boundary value problem for nondivergence second order parabolic equations with discontinuous coefficients”, Mat. Sb. (N.S.), 131(173):4(12) (1986), 477–500; Math. USSR-Sb., 59:2 (1988), 471–495

Citation in format AMSBIB
\Bibitem{AlkMam86} \by Yu.~A.~Alkhutov, I.~T.~Mamedov \paper The first boundary value problem for nondivergence second order parabolic equations with discontinuous coefficients \jour Mat. Sb. (N.S.) \yr 1986 \vol 131(173) \issue 4(12) \pages 477--500 \mathnet{http://mi.mathnet.ru/msb1974} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=881909} \zmath{https://zbmath.org/?q=an:0663.35033} \transl \jour Math. USSR-Sb. \yr 1988 \vol 59 \issue 2 \pages 471--495 \crossref{https://doi.org/10.1070/SM1988v059n02ABEH003147} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Kamynin V., “Asymptotic-Behavior of Solutions of the Cauchy-Problem for Non-Divergence Parabolic Equations”, 316, no. 4, 1991, 807–811
2. Kamynin V., “Passage to the Limit in the Inverse Problem for Nondivergent Parabolic Equations with a Final Overdetermination Condition”, Differ. Equ., 28:2 (1992), 213–218
3. Gasanova I., “On the Holder Property of Derivatives of Solutions to 2nd-Order Parabolic Equations in Nontube Domains”, Differ. Equ., 30:1 (1994), 100–109
4. Guochun Wen, Benteng Zou, “Estimates of solutions of initial-irregular oblique derivative problems for linear parabolic equations of second order with measurable coefficients”, Sci China Ser A, 41:11 (1998), 1163
5. Guochun Wen, Maoying Tain, “Initial-oblique derivative problems for nonlinear parabolic equations with measurable coefficients”, Communications in Nonlinear Science and Numerical Simulation, 3:2 (1998), 109
6. Guochun Wen, “Initial-irregular oblique derivative problems for nonlinear parabolic systems of second order equations with measurable coefficients”, Sci China Ser A, 42:7 (1999), 681
7. Guochun Wen, Zuoliang Xu, “Oblique derivative problems for nonlinear elliptic systems with measurable coefficients”, Communications in Nonlinear Science and Numerical Simulation, 6:2 (2001), 93
8. V. L. Kamynin, “On the Unique Solvability of an Inverse Problem for Parabolic Equations under a Final Overdetermination Condition”, Math. Notes, 73:2 (2003), 202–211
9. V. L. Kamynin, “On the inverse problem of determining the right-hand side of a parabolic equation under an integral overdetermination condition”, Math. Notes, 77:4 (2005), 482–493
10. Guochun Wen, Dechang Chen, “Oblique derivative boundary value problems for nonlinear elliptic equations of second order with measurable coefficients in high dimensional domains”, Communications in Nonlinear Science and Numerical Simulation, 10:5 (2005), 559
11. Guo Chun Wen, DeChang Chen, “Mixed boundary value problems for nonlinear elliptic equations of second order with measurable coefficients in high dimensional domains”, Complex Variables, 51:3 (2006), 267
12. Guochun Wen, Dechang Chen, “Some boundary value problems for nonlinear elliptic equations of second order in high-dimensional domains”, Applicable Analysis, 85:9 (2006), 1011
13. Gadjiev T.S., Gasimova E.R., “On the Smoothness of a Solution of the First Boundary-Value Problem for Second-Order Degenerate Elliptic-Parabolic Equations”, Ukr. Math. J., 60:6 (2008), 831–847
14. BOUBAKER-KHALED SADALLAH, “REGULARITY OF A PARABOLIC EQUATION SOLUTION IN A NONSMOOTH AND UNBOUNDED DOMAIN”, JAZ, 84:02 (2008)
15. Erisova I.A., “Convergence of Solutions of Backward Stochastic Equations”, Ukr. Math. J., 61:7 (2009), 1093–1112
16. I. T. Mamedov, “First boundary-value problem for second-order elliptic-parabolic equations with discontinuous coefficients”, Journal of Mathematical Sciences, 190:1 (2013), 104–134
17. Kamynin V.L., “Ob odnoznachnoi razreshimosti obratnoi zadachi opredeleniya starshego koeffitsienta v parabolicheskom uravnenii”, Differentsialnye uravneniya, 47:1 (2011), 92–102
18. Kamynin V.L., “Unique Solvability of the Inverse Problem of Determination of the Leading Coefficient in a Parabolic Equation”, Differ. Equ., 47:1 (2011), 91–101
19. Guochun Wen, Dechang Chen, “Boundary Value Problems for Nonlinear Elliptic Equations of Second Order in High Dimensional Domains”, AM, 04:12 (2013), 1651
20. Louanas Bouzidi, Arezki Kheloufi, “Global in time results for a parabolic equation solution in non-rectangular domains”, Zhurn. SFU. Ser. Matem. i fiz., 13:3 (2020), 257–274
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