Persons: Alkhutov, Yuriy Alexandrovich

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Alkhutov, Yuriy Alexandrovich

Statistics Math-Net.Ru
Total publications:	37
Scientific articles:	34
Presentations:	6

Number of views:
This page:	5668
Abstract pages:	12348
Full texts:	4015
References:	1331

Professor

Doctor of physico-mathematical sciences (1992)

Speciality:

01.01.02 (Differential equations, dynamical systems, and optimal control)

E-mail:

Keywords:

elliptic and parabolic equations; solvability of a boundary value problem; a priori estimate; boundary properties of solutions; embedding theorem; capacity; removable singularities of solutions; maximal function.

Subject:

The class of nondivergent elliptic equations of the second order with Wiener test regularity of a boundary point in terms of introduced function of ellipticity was described. This class сontain equations with dicontinuous coefficients. The parabolic analog of Cordes condition guaranteeing unique solvability of the first boundary value problem for nondivergent parabolic equations of the second order in the Sobolev space $W^{2,1}_{2,0}$ was found (with I. T. Mamedov). Necessary and sufficient condition on a boundary for unique $L_p$–solvability of the Dirichlet problem together with the corresponding coercive estimate for divergent elliptic equations of the second order was obtained. The smoothness at a point for solutions of parabolic equations of the second order under minimal assumptions on coefficients was investigated. Inner and boundary properties for solutions of quasilinear elliptic equations for integrands $|\xi|^{p(x)}$ were studied. The Holder property for solutions of degenerate elliptic equations of the second order with a weight that is not satisfying neither Muckenhoupt condition nor double condition was proved (with V. V. Zhikov). Interesting feature of these equations is absent of Harnack inequality for positive solutions.

Biography

Graduated from department of applied mathematics of Azerbaijan Institute of Oil and Chemistry in 1979. Ph.D. thesis was defended in 1982. D.Sci thesis was defended in 1992.

Main publications:

Alkhutov Yu. A., Mamedov I. T. Pervaya kraevaya zadacha dlya nedivergentnykh parabolicheskikh uravnenii vtorogo poryadka s razryvnymi koeffitsientami // Matem. cbornik, 1986, 173(4), 477–500.
Alkhutov Yu. A. Ustranimye osobennosti reshenii parabolicheskikh uravnenii vtorogo poryadka // Matem. zametki, 1991, 50(5), 9–17.
Alkhutov Yu. A. Neravenstvo Kharnaka i gelderovost reshenii nelineinykh ellipticheskikh uravnenii s nestandartnym usloviem rosta // Differents. uravneniya, 1997, 33(12), 1651–1660.
Alkhutov Yu. A. $L_p$&-otsenki resheniya zadachi Dirikhle dlya ellipticheskikh uravnenii vtorogo poryadka // Matem. cbornik, 1998, 189(1), 3–20.
Alkhutov Yu. A., Zhikov V. V. O gelderovosti reshenii vyrozhdayuschikhsya ellipticheskikh uravnenii // Doklady RAN, 2001, 378(5), 583–588.

https://www.mathnet.ru/eng/person8561

List of publications on Google Scholar

List of publications on ZentralBlatt

https://mathscinet.ams.org/mathscinet/MRAuthorID/224718

	Publications in Math-Net.Ru	Citations
	2024
1.	Yu. A. Alkhutov, G. A. Chechkin, “On the Boyarsky–Meyers estimate for the solution of the Dirichlet problem for a second-order linear elliptic equation with drift”, CMFD, 70:1 (2024), 1–14
2.	Yu. A. Alkhutov, G. A. Chechkin, “Multidimensional Zaremba problem for the $p(\,\cdot\,)$-laplace equation. A Boyarsky–Meyers estimate”, TMF, 218:1 (2024), 3–22 ; Theoret. and Math. Phys., 218:1 (2024), 1–18
	2023
3.	Yu. A. Alkhutov, C. D. Apice, M. A. Kisatov, A. G. Chechkina, “On higher integrability of the gradient of solutions to the Zaremba problem for $p$-Laplace equation”, Dokl. RAN. Math. Inf. Proc. Upr., 512 (2023), 47–51 ; Dokl. Math., 108:1 (2023), 282–285
	2022
4.	Yu. A. Alkhutov, A. G. Chechkina, “Many-dimensional Zaremba problem for an inhomogeneous $p$-Laplace equation”, Dokl. RAN. Math. Inf. Proc. Upr., 505 (2022), 37–41 ; Dokl. Math., 106:1 (2022), 243–246	6
	2021
5.	Yu. A. Alkhutov, G. A. Chechkin, “Increased integrability of the gradient of the solution to the Zaremba problem for the Poisson equation”, Dokl. RAN. Math. Inf. Proc. Upr., 497 (2021), 3–6 ; Dokl. Math., 103:2 (2021), 69–71	11
6.	Yu. A. Alkhutov, M. D. Surnachev, “Interior and boundary continuity of $p(x)$-harmonic functions”, Zap. Nauchn. Sem. POMI, 508 (2021), 7–38
	2020
7.	Yu. A. Alkhutov, M. D. Surnachev, “Hölder Continuity and Harnack's Inequality for $p(x)$-Harmonic Functions”, Trudy Mat. Inst. Steklova, 308 (2020), 7–27 ; Proc. Steklov Inst. Math., 308 (2020), 1–21	6
8.	Yu. A. Alkhutov, M. D. Surnachev, “Estimates of the fundamental solution for an elliptic equation in divergence form with drift”, Zap. Nauchn. Sem. POMI, 489 (2020), 7–35	2
9.	Yu. A. Alkhutov, M. D. Surnachev, “Harnack inequality for the elliptic $p(x)$-Laplacian with a three-phase exponent $p(x)$”, Zh. Vychisl. Mat. Mat. Fiz., 60:8 (2020), 1329–1338 ; Comput. Math. Math. Phys., 60:8 (2020), 1284–1293
	2019
10.	Yu. A. Alkhutov, M. D. Surnachev, “Behavior of solutions of the Dirichlet Problem for the $ p(x)$-Laplacian at a boundary point”, Algebra i Analiz, 31:2 (2019), 88–117 ; St. Petersburg Math. J., 31:2 (2019), 251–271	19
11.	Yu. A. Alkhutov, M. D. Surnachev, “Harnack's inequality for the $p(x)$-Laplacian with a two-phase exponent $p(x)$”, Tr. Semim. im. I. G. Petrovskogo, 32 (2019), 8–56 ; J. Math. Sci. (N. Y.), 244:2 (2020), 116–147	9
	2014
12.	Yu. A. Alkhutov, V. N. Denisov, “Necessary and sufficient condition for the stabilization of the solution of a mixed problem for nondivergence parabolic equations to zero”, Tr. Mosk. Mat. Obs., 75:2 (2014), 277–308 ; Trans. Moscow Math. Soc., 75 (2014), 233–258	5
13.	Yu. A. Alkhutov, V. V. Zhikov, “Existence and uniqueness theorems for solutions of parabolic equations with a variable nonlinearity exponent”, Mat. Sb., 205:3 (2014), 3–14 ; Sb. Math., 205:3 (2014), 307–318	27
	2013
14.	Yu. A. Alkhutov, “Hölder continuity of solutions of nondivergent degenerate second-order elliptic equations”, Tr. Semim. im. I. G. Petrovskogo, 29 (2013), 5–42 ; J. Math. Sci. (N. Y.), 197:2 (2014), 151–174
	2012
15.	Yu. A. Alkhutov, E. A. Khrenova, “Harnack inequality for a class of second-order degenerate elliptic equations”, Trudy Mat. Inst. Steklova, 278 (2012), 7–15 ; Proc. Steklov Inst. Math., 278 (2012), 1–9	10
	2011
16.	Yu. A. Alkhutov, V. V. Zhikov, “Hölder continuity of solutions of parabolic equations with variable nonlinearity exponent”, Tr. Semim. im. I. G. Petrovskogo, 28 (2011), 8–74 ; J. Math. Sci. (N. Y.), 179:3 (2011), 347–389	18
	2010
17.	Yu. A. Alkhutov, V. V. Zhikov, “Existence theorems for solutions of parabolic equations with variable order of nonlinearity”, Trudy Mat. Inst. Steklova, 270 (2010), 21–32 ; Proc. Steklov Inst. Math., 270 (2010), 15–26	31
	2009
18.	Yu. A. Alkhutov, A. N. Gordeev, “$L_p$-solubility of the Dirichlet problem for the heat operator”, Uspekhi Mat. Nauk, 64:1(385) (2009), 137–138 ; Russian Math. Surveys, 64:1 (2009), 131–133
	2008
19.	Yu. A. Alkhutov, O. V. Krasheninnikova, “On the Continuity of Solutions to Elliptic Equations with Variable Order of Nonlinearity”, Trudy Mat. Inst. Steklova, 261 (2008), 7–15 ; Proc. Steklov Inst. Math., 261 (2008), 1–10	22
	2005
20.	Yu. A. Alkhutov, “Hölder continuity of $p(x)$-harmonic functions”, Mat. Sb., 196:2 (2005), 3–28 ; Sb. Math., 196:2 (2005), 147–171	25
	2004
21.	Yu. A. Alkhutov, O. V. Krasheninnikova, “Continuity at boundary points of solutions of quasilinear elliptic equations with a non-standard growth condition”, Izv. RAN. Ser. Mat., 68:6 (2004), 3–60 ; Izv. Math., 68:6 (2004), 1063–1117	65
	2002
22.	Yu. A. Alkhutov, “$L_p$-solubility of the Dirichlet problem for the heat equation in non-cylindrical domains”, Mat. Sb., 193:9 (2002), 3–40 ; Sb. Math., 193:9 (2002), 1243–1279	4
	1998
23.	Yu. A. Alkhutov, V. V. Zhikov, “The leading term of the spectral asymptotics for the Kohn–Laplace operator in a bounded domain”, Mat. Zametki, 64:4 (1998), 493–505 ; Math. Notes, 64:4 (1998), 429–439	1
24.	Yu. A. Alkhutov, “$L_p$-estimates of the solution of the Dirichlet problem for second-order elliptic equations”, Mat. Sb., 189:1 (1998), 3–20 ; Sb. Math., 189:1 (1998), 1–17	10
	1997
25.	Yu. A. Alkhutov, “The Harnack inequality and the Hölder property of solutions of nonlinear elliptic equations with a nonstandard growth condition”, Differ. Uravn., 33:12 (1997), 1651–1660 ; Differ. Equ., 33:12 (1997), 1653–1663	16
	1995
26.	Yu. A. Alkhutov, “The behavior of solutions of parabolic second-order equations in noncylindrical domains”, Dokl. Akad. Nauk, 345:5 (1995), 583–585
	1992
27.	Yu. A. Alkhutov, V. A. Kondratiev, “Solvability of the Dirichlet problem for second-order elliptic equations in a convex domain”, Differ. Uravn., 28:5 (1992), 806–818 ; Differ. Equ., 28:5 (1992), 650–662	13
	1991
28.	Yu. A. Alkhutov, “Removable singularities of solutions of second-order parabolic equations”, Mat. Zametki, 50:5 (1991), 9–17 ; Math. Notes, 50:5 (1991), 1097–1103	5
29.	Yu. A. Alkhutov, “Smoothness and limiting properties of solutions of a second-order parabolic equation”, Mat. Zametki, 50:4 (1991), 150–152 ; Math. Notes, 50:4 (1991), 1085–1087
	1990
30.	Yu. A. Alkhutov, “Local properties of solutions of non-divergent parabolic equations of second order”, Uspekhi Mat. Nauk, 45:5(275) (1990), 175–176 ; Russian Math. Surveys, 45:5 (1990), 221–222
	1988
31.	Yu. A. Alkhutov, “Removable singularities of solutions of parabolic equations”, Uspekhi Mat. Nauk, 43:1(259) (1988), 189–190 ; Russian Math. Surveys, 43:1 (1988), 229–230
	1986
32.	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	26
	1985
33.	Yu. A. Alkhutov, I. T. Mamedov, “Some properties of the solutions of the first boundary value problem for parabolic equations with discontinuous coefficients”, Dokl. Akad. Nauk SSSR, 284:1 (1985), 11–16	2
	1981
34.	Yu. A. Alkhutov, “Regularity of boundary points relative to the Dirichlet problem for second-order elliptic equations”, Mat. Zametki, 30:3 (1981), 333–342 ; Math. Notes, 30:3 (1981), 655–660	3

	2019
35.	Yu. A. Alkhutov, V. F. Butuzov, V. V. Kozlov, A. A. Kon'kov, A. V. Mikhalev, E. I. Moiseev, E. V. Radkevich, N. Kh. Rozov, V. A. Sadovnichii, I. N. Sergeev, M. D. Surnachev, R. N. Tikhomirov, V. N. Chubarikov, T. A. Shaposhnikova, A. A. Shkalikov, “Vasilii Vasilievich Zhikov”, Tr. Semim. im. I. G. Petrovskogo, 32 (2019), 5–7 ; J. Math. Sci. (N. Y.), 244:2 (2020), 113–115
	2018
36.	Yu. A. Alkhutov, I. V. Astashova, V. I. Bogachev, V. N. Denisov, V. V. Kozlov, S. E. Pastukhova, A. L. Piatnitski, V. A. Sadovnichii, A. M. Stepin, A. S. Shamaev, A. A. Shkalikov, “Vasilii Vasil'evich Zhikov (obituary)”, Uspekhi Mat. Nauk, 73:3(441) (2018), 169–176 ; Russian Math. Surveys, 73:3 (2018), 533–542

Presentations in Math-Net.Ru

1.	Elliptic Equations and Meyers Estimates Yu. A. Alkhutov, G. A. Chechkin International Conference Dedicated to the 100th Anniversary of the Birthday of V. S. Vladimirov (Vladimirov-100) January 10, 2023 18:00
2.	Boundary regularity for solutions of second-order elliptic equations with partial Muckenhoupt weight. Yu. A. Alkhutov, M. D. Surnachev Seminar on nonlinear problems of partial differential equations and mathematical physics December 7, 2021 18:00
3.	On regularity of p(x)-harmonic functions Yu. A. Alkhutov, M. D. Surnachev Mathematical Colloquium of the Bauman Moscow State Technical University November 25, 2021 17:30
4.	Elliptic and parabolic equations of the second order with nonstandard growth condition Yu. A. Alkhutov Seminar on nonlinear problems of partial differential equations and mathematical physics April 20, 2021 19:30
5.	Sharp estimates of solutions to the Dirichlet problem for p(x)- harmonic functions in a neighborhood of the boundary conical point Yu. A. Alkhutov, M. V. Borsuk International Conference on Mathematical Control Theory and Mechanics July 6, 2015 12:40
6.	Degenerate elliptic equations in the presence of Lavrent'ev effect Yu. A. Alkhutov International Conference on Differential Equations and Dynamical Systems July 8, 2014 14:30

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