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## Gushchin, Anatoliĭ Konstantinovich

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 Author ID: gushchin.anatolii-konstantinovich Published as: Gushchin, A. K.; Gushchin, Anatolii K.; Gushchin, Anatoliĭ Konstantinovich
 Documents Indexed: 80 Publications since 1967, including 1 Book
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#### Co-Authors

 48 single-authored 21 Mikhajlov, Valentin Petrovich 8 Mikhaĭlov, V. P. 6 Vladimirov, Vasiliĭ Sergeevich 5 Volovich, Igor’ Vasil’evich 4 Drozhzhinov, Yuriĭ Nikolaevich 4 Zharinov, Victor Victorovich 3 Il’in, Vladimir Aleksandrovich 2 Bogoyavlenskij, Oleg Igorevich 2 Dezin, Alekseĭ Alekseevich 2 Mikhajlov, Yu. A. 2 Millionshchikov, Vladimir Mikhaĭlovich 2 Moiseev, Evgeniĭ Ivanovich 2 Pal’tsev, B. V. 2 Zav’yalov, Boris Ivanovich 1 Marchuk, Guriĭ Ivanovich 1 Maslennikova, Vera Nikolaevna 1 Mikhailov, V. I. 1 Nikol’skiĭ, Sergeĭ Mikhaĭlovich 1 Pontryagin, Lev Semënovich 1 Romanko, V. K. 1 Samarskiĭ, Aleksandr Andreevich 1 Sergeev, Armen Glebovich
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#### Serials

 12 Soviet Mathematics. Doklady 10 Mathematics of the USSR, Sbornik 10 Sbornik: Mathematics 8 Doklady Mathematics 8 Proceedings of the Steklov Institute of Mathematics 6 Trudy Matematicheskogo Instituta Imeni V. A. Steklova 4 Differential Equations 4 Matematicheskiĭ Sbornik. Novaya Seriya 3 Differentsial’nye Uravneniya 2 Russian Mathematical Surveys 2 Sibirskiĭ Matematicheskiĭ Zhurnal 2 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 1 Theoretical and Mathematical Physics 1 Applied Mathematics and Optimization 1 Siberian Mathematical Journal 1 Russian Academy of Sciences. Sbornik. Mathematics 1 Russian Academy of Sciences. Doklady. Mathematics 1 Lektsionnye Kursy NOTs
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#### Fields

 69 Partial differential equations (35-XX) 6 History and biography (01-XX) 4 Operator theory (47-XX) 3 Functional analysis (46-XX) 2 Mechanics of particles and systems (70-XX) 1 General and overarching topics; collections (00-XX) 1 Integral equations (45-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Astronomy and astrophysics (85-XX)

#### Citations contained in zbMATH

40 Publications have been cited 160 times in 71 Documents Cited by Year
On the Dirichlet problem for a second-order elliptic equation. Zbl 0683.35013
Gushchin, A. K.
1990
A criterion for uniform stabilization of solutions of the second mixed problem for a parabolic equation. Zbl 0509.35045
Gushchin, A. K.
1982
The Dirichlet problem for a second-order elliptic equation with an $$L_{p}$$ boundary function. Zbl 1244.35038
Gushchin, A. K.
2012
The compactness condition for a class of operators and its application to the investigation of the solvability of nonlocal problems for elliptic equations. Zbl 1085.35058
Gushchin, A. K.
2002
On the existence of boundary values of solutions of an elliptic equation. Zbl 0781.35020
Gushchin, A. K.; Mikhajlov, V. P.
1992
On the continuity of the solutions of a class of non-local problems for an elliptic equation. Zbl 0849.35025
Gushchin, A. K.; Mikhailov, V. I.
1995
$$L_p$$-estimates for the nontangential maximal function of the solution to a second-order elliptic equation. Zbl 1375.35141
Gushchin, Anatolii K.
2016
On boundary values in $$L_ p$$, $$p>1$$, of solutions of elliptic equations. Zbl 0453.35035
Gushchin, A. K.; Mikhajlov, V. P.
1980
Solvability of the Dirichlet problem for an inhomogeneous second-order elliptic equation. Zbl 1333.35035
Gushchin, A. K.
2015
A strengthening of the interior Hölder continuity property for solutions of the Dirichlet problem for a second-order elliptic equation. Zbl 1155.35325
Gushchin, A. K.
2008
Additional chapters of the course “Equations of mathematical physics”. Zbl 1278.35001
Mikhaĭlov, V. P.; Gushchin, A. K.
2007
Estimates of the nontangential maximal function for solutions of a second-order elliptic equation. Zbl 1271.35014
Gushchin, A. K.
2012
Solvability of the Dirichlet problem for a second-order elliptic equation with a boundary function from $$L_{p}$$. Zbl 1272.35081
Gushchin, A. K.
2011
On the interior smoothness of solutions to second-order elliptic equations. Zbl 1114.35037
Gushchin, A. K.
2005
On solvability of nonlocal problems for a second-order elliptic equation. Zbl 0827.35034
Gushchin, A. K.; Mikhajlov, V. P.
1994
The rate of stabilization of a solution of a parabolic equation in an unbounded region. Zbl 0234.35041
Gushchin, A. K.
1970
Boundary value problems of mathematical physics. Zbl 0627.35080
Bogoyavlenskij, O. I.; Vladimirov, V. S.; Volovich, I. V.; Gushchin, A. K.; Drozhzhinov, Yu. N.; Zharinov, V. V.; Mikhajlov, V. P.
1986
On the speed of stabilization of the solution of a boundary problem for a parabolic equation. Zbl 0183.10802
Gushchin, A. K.
1969
The Luzin area integral and the nontangential maximal function for solutions to a second-order elliptic equation. Zbl 1402.35100
Gushchin, A. K.
2018
V. A. Steklov’s work on equations of mathematical physics and development of his results in this field. Zbl 1339.35204
Gushchin, A. K.
2015
Some properties of the solutions of the Dirichlet problem for a second-order elliptic equation. Zbl 0918.35044
Gushchin, A. K.
1998
On the stabilization of the solution of a parabolic equation. Zbl 0197.37501
Gushchin, A. K.
1968
A criterion for the existence of $$L_p$$ boundary values of solutions to an elliptic equation. Zbl 1401.35059
Gushchin, A. K.
2018
On uniform stabilization of the solution of the second mixed problem for a second order parabolic equation. Zbl 0645.35038
Gushchin, A. K.; Mikhajlov, V. P.; Mikhajlov, Yu. A.
1987
On the uniform stabilization of solutions of the second mixed problem for a parabolic equation. Zbl 0554.35055
Gushchin, A. K.
1984
Certain properties of the generalized solution of a second order boundary value problem for a parabolic equation. Zbl 0323.35041
Gushchin, A. K.
1975
Smoothness of solutions to the Dirichlet problem for a second-order elliptic equation with a square integrable boundary function. Zbl 1161.35352
Gushchin, A. K.
2007
On the univalent solvability of nonlocal problems for an elliptic equation. Zbl 0896.35035
Gushchin, A. K.; Mikhailov, V. P.
1996
Boundary value problems of mathematical physics. Zbl 0698.35122
Bogoyavlenskij, O. I.; Vladimirov, V. S.; Volovich, I. V.; Gushchin, A. K.; Drozhzhinov, Yu. N.; Zharinov, V. V.; Mikhajlov, V. P.
1988
On uniform stabilization of the solution of the Cauchy problem for a second order hyperbolic equation. Zbl 0584.35064
Gushchin, A. K.; Mikhaĭlov, V. P.
1986
On uniform stabilization of the solution of the Cauchy problem for a second order hyperbolic equation. Zbl 0567.35052
Gushchin, A. K.; Mikhaĭlov, V. P.
1984
On the behaviour as $$t \to \infty$$ of solutions of the second mixed problem for a second-order parabolic equation. Zbl 0452.35046
Gushchin, A. K.
1980
Stabilization of the solutions of the second boundary value problem for a second order parabolic equation. Zbl 0387.35007
Gushchin, A. K.
1978
On an estimate of the Dirichlet integral in unbounded domains. Zbl 0368.35013
Gushchin, A. K.
1978
Some properties of a generalized solution of the second boundaryvalue problem for a parabolic equation. Zbl 0338.35047
Gushchin, A. K.
1976
On estimates of the solutions of boundary value problems for a parabolic equation of second order. Zbl 0296.35044
Gushchin, A. K.
1975
Über Schranken der Lösungen von Randwertproblemen für eine parabolische Gleichung zweiter Ordnung. Zbl 0288.35029
Gushchin, A. K.
1973
Stabilization of solutions of Cauchy’s problem for a parabolic equation. Zbl 0266.35037
Gushchin, A. K.; Mikhajlov, V. P.
1973
On stabilization of the solution of the Cauchy problem for a parabolic equation. Zbl 0212.13001
Gushchin, A. K.; Mikhajlov, V. P.
1970
Gewisse Abschätzungen der Lösungen von Randwertproblemen für die Wärmeleitungsgleichung in einem nichtbeschränkten Gebiet. Zbl 0165.44103
Gushchin, A. K.
1967
The Luzin area integral and the nontangential maximal function for solutions to a second-order elliptic equation. Zbl 1402.35100
Gushchin, A. K.
2018
A criterion for the existence of $$L_p$$ boundary values of solutions to an elliptic equation. Zbl 1401.35059
Gushchin, A. K.
2018
$$L_p$$-estimates for the nontangential maximal function of the solution to a second-order elliptic equation. Zbl 1375.35141
Gushchin, Anatolii K.
2016
Solvability of the Dirichlet problem for an inhomogeneous second-order elliptic equation. Zbl 1333.35035
Gushchin, A. K.
2015
V. A. Steklov’s work on equations of mathematical physics and development of his results in this field. Zbl 1339.35204
Gushchin, A. K.
2015
The Dirichlet problem for a second-order elliptic equation with an $$L_{p}$$ boundary function. Zbl 1244.35038
Gushchin, A. K.
2012
Estimates of the nontangential maximal function for solutions of a second-order elliptic equation. Zbl 1271.35014
Gushchin, A. K.
2012
Solvability of the Dirichlet problem for a second-order elliptic equation with a boundary function from $$L_{p}$$. Zbl 1272.35081
Gushchin, A. K.
2011
A strengthening of the interior Hölder continuity property for solutions of the Dirichlet problem for a second-order elliptic equation. Zbl 1155.35325
Gushchin, A. K.
2008
Additional chapters of the course “Equations of mathematical physics”. Zbl 1278.35001
Mikhaĭlov, V. P.; Gushchin, A. K.
2007
Smoothness of solutions to the Dirichlet problem for a second-order elliptic equation with a square integrable boundary function. Zbl 1161.35352
Gushchin, A. K.
2007
On the interior smoothness of solutions to second-order elliptic equations. Zbl 1114.35037
Gushchin, A. K.
2005
The compactness condition for a class of operators and its application to the investigation of the solvability of nonlocal problems for elliptic equations. Zbl 1085.35058
Gushchin, A. K.
2002
Some properties of the solutions of the Dirichlet problem for a second-order elliptic equation. Zbl 0918.35044
Gushchin, A. K.
1998
On the univalent solvability of nonlocal problems for an elliptic equation. Zbl 0896.35035
Gushchin, A. K.; Mikhailov, V. P.
1996
On the continuity of the solutions of a class of non-local problems for an elliptic equation. Zbl 0849.35025
Gushchin, A. K.; Mikhailov, V. I.
1995
On solvability of nonlocal problems for a second-order elliptic equation. Zbl 0827.35034
Gushchin, A. K.; Mikhajlov, V. P.
1994
On the existence of boundary values of solutions of an elliptic equation. Zbl 0781.35020
Gushchin, A. K.; Mikhajlov, V. P.
1992
On the Dirichlet problem for a second-order elliptic equation. Zbl 0683.35013
Gushchin, A. K.
1990
Boundary value problems of mathematical physics. Zbl 0698.35122
Bogoyavlenskij, O. I.; Vladimirov, V. S.; Volovich, I. V.; Gushchin, A. K.; Drozhzhinov, Yu. N.; Zharinov, V. V.; Mikhajlov, V. P.
1988
On uniform stabilization of the solution of the second mixed problem for a second order parabolic equation. Zbl 0645.35038
Gushchin, A. K.; Mikhajlov, V. P.; Mikhajlov, Yu. A.
1987
Boundary value problems of mathematical physics. Zbl 0627.35080
Bogoyavlenskij, O. I.; Vladimirov, V. S.; Volovich, I. V.; Gushchin, A. K.; Drozhzhinov, Yu. N.; Zharinov, V. V.; Mikhajlov, V. P.
1986
On uniform stabilization of the solution of the Cauchy problem for a second order hyperbolic equation. Zbl 0584.35064
Gushchin, A. K.; Mikhaĭlov, V. P.
1986
On the uniform stabilization of solutions of the second mixed problem for a parabolic equation. Zbl 0554.35055
Gushchin, A. K.
1984
On uniform stabilization of the solution of the Cauchy problem for a second order hyperbolic equation. Zbl 0567.35052
Gushchin, A. K.; Mikhaĭlov, V. P.
1984
A criterion for uniform stabilization of solutions of the second mixed problem for a parabolic equation. Zbl 0509.35045
Gushchin, A. K.
1982
On boundary values in $$L_ p$$, $$p>1$$, of solutions of elliptic equations. Zbl 0453.35035
Gushchin, A. K.; Mikhajlov, V. P.
1980
On the behaviour as $$t \to \infty$$ of solutions of the second mixed problem for a second-order parabolic equation. Zbl 0452.35046
Gushchin, A. K.
1980
Stabilization of the solutions of the second boundary value problem for a second order parabolic equation. Zbl 0387.35007
Gushchin, A. K.
1978
On an estimate of the Dirichlet integral in unbounded domains. Zbl 0368.35013
Gushchin, A. K.
1978
Some properties of a generalized solution of the second boundaryvalue problem for a parabolic equation. Zbl 0338.35047
Gushchin, A. K.
1976
Certain properties of the generalized solution of a second order boundary value problem for a parabolic equation. Zbl 0323.35041
Gushchin, A. K.
1975
On estimates of the solutions of boundary value problems for a parabolic equation of second order. Zbl 0296.35044
Gushchin, A. K.
1975
Über Schranken der Lösungen von Randwertproblemen für eine parabolische Gleichung zweiter Ordnung. Zbl 0288.35029
Gushchin, A. K.
1973
Stabilization of solutions of Cauchy’s problem for a parabolic equation. Zbl 0266.35037
Gushchin, A. K.; Mikhajlov, V. P.
1973
The rate of stabilization of a solution of a parabolic equation in an unbounded region. Zbl 0234.35041
Gushchin, A. K.
1970
On stabilization of the solution of the Cauchy problem for a parabolic equation. Zbl 0212.13001
Gushchin, A. K.; Mikhajlov, V. P.
1970
On the speed of stabilization of the solution of a boundary problem for a parabolic equation. Zbl 0183.10802
Gushchin, A. K.
1969
On the stabilization of the solution of a parabolic equation. Zbl 0197.37501
Gushchin, A. K.
1968
Gewisse Abschätzungen der Lösungen von Randwertproblemen für die Wärmeleitungsgleichung in einem nichtbeschränkten Gebiet. Zbl 0165.44103
Gushchin, A. K.
1967
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#### Cited by 51 Authors

 13 Gushchin, Anatoliĭ Konstantinovich 5 Denisov, Vasiliĭ Nikolaevich 4 Grigor’yan, Alexander Asaturovich 4 Skubachevskij, Alexander L. 3 Andreucci, Daniele 3 Dumanyan, Vahram Zh. 3 Gurevich, Pavel L. 3 Jangveladze, Temur A. 3 Mukminov, Farit Khamzaevich 3 Tedeev, Anatoliĭ Fedorovich 3 Zharinov, Victor Victorovich 2 Chabrowski, Jan H. 2 Denisov, V. N. 2 Ishige, Kazuhiro 2 Lobjanidze, G. B. 2 Vlasov, Vladimir Ivanovich 1 Alkhutov, Yuriy Alexandrovich 1 Andriyanova, Èlina Radikovna 1 Barlow, Martin T. 1 Beĭlina, Natal’ya Viktorovna 1 Bezrodnykh, Sergeĭ I. 1 Buhrii, Nataliya V. 1 Buhrii, Oleh 1 Cirmi, Giuseppa Rita 1 Filinovskiĭ, Alexeĭ Vladislavovich 1 Galtsev, Oleg V. 1 Gilding, Brian H. 1 Guschin, A. K. 1 Gusev, Nikolaĭ Anatol’evich 1 Gutlyanskiĭ, Vladimir Ya. 1 Huang, Xueping 1 Katanaev, Mikhaĭl Orinovich 1 Kiguradze, Zurab V. 1 Kirichenko, S. V. 1 Kochubeĭ, Anatoliĭ Naumovych 1 Kostin, Andrey B. 1 Kozhanov, Aleksandr Ivanovich 1 Kumagai, Takashi 1 Leonardi, Salvatore 1 Lobjanidze, George 1 Meirmanov, Anvarbek Mukatovich 1 Mesloub, Said 1 Murata, Minoru 1 Muravnik, Andreĭ Borisovich 1 Nesmelova, Ol’ga Vladimirovna 1 Nunez, Manuel A. 1 Petrushko, Igor’ Meletievich 1 Rozkosz, Andrzej 1 Ryazanov, Vladimir Il’ich 1 Telcs, András 1 Uspenskiĭ, Stanislav Viktorovich
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#### Cited in 32 Serials

 10 Journal of Mathematical Sciences (New York) 6 Theoretical and Mathematical Physics 6 Sbornik: Mathematics 6 Proceedings of the Steklov Institute of Mathematics 4 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 3 Journal of Differential Equations 3 Doklady Mathematics 3 Differential Equations 2 Journal of Mathematical Analysis and Applications 2 Mathematical Notes 2 Rendiconti del Seminario Matematico della Università di Padova 2 Siberian Mathematical Journal 2 Transactions of the Moscow Mathematical Society 2 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 1 Mathematical Methods in the Applied Sciences 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 The Annals of Probability 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Applied Mathematics and Optimization 1 Journal of the Mathematical Society of Japan 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Communications in Partial Differential Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Stochastic Processes and their Applications 1 Bulletin of the American Mathematical Society. New Series 1 Turkish Journal of Mathematics 1 Fractional Calculus & Applied Analysis 1 Complex Variables and Elliptic Equations 1 Discrete and Continuous Dynamical Systems. Series S 1 Eurasian Mathematical Journal 1 International Journal of Partial Differential Equations 1 Open Mathematics
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#### Cited in 21 Fields

 59 Partial differential equations (35-XX) 8 Global analysis, analysis on manifolds (58-XX) 5 Ordinary differential equations (34-XX) 4 Probability theory and stochastic processes (60-XX) 3 Functional analysis (46-XX) 3 Operator theory (47-XX) 3 Fluid mechanics (76-XX) 2 Field theory and polynomials (12-XX) 2 Potential theory (31-XX) 2 Relativity and gravitational theory (83-XX) 1 History and biography (01-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 Measure and integration (28-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Differential geometry (53-XX) 1 Numerical analysis (65-XX) 1 Mechanics of deformable solids (74-XX) 1 Quantum theory (81-XX)