Research interests

 

• homogenization theory of nonlinear partial differential equations;
• Г-convergence of integral functionals and G-convergence of nonlinear differential operators;
• qualitative properties of solutions of nonlinear high-order equations;
• existence and properties of solutions of nonlinear equations with L^1 -data.
  

Diplomas

1979 - Diploma on graduation of Donetsk State University;

1985 - PhD diploma in Physical and Mathematical Sciences, Institute of Applied Mathematics and Mechanics Аcad. Sci. UkrSSR;

1993 - Certificate of Senior Research Scientist by speciality "Differential Equations", Institute of Applied Mathematics and Mechanics of Acad. Sci. of Ukraine;

1995 - Diploma of Doctor of Sciences in Physics and Mathematics, Institute of Applied Mathematics and Mechanics of NAS of Ukraine.

Career

since March, 2006 - Vice-Director in Science, Institute of Applied Mathematics and Mechanics;

2005-present time - Head of the Department of Nonlinear Analysis, Institute of Applied Mathematics and Mechanics;

1979-2005 - post graduate student, engineer, junior research scientist, research scientist, senior research scientist, leading research scientist at the Department of Nonlinear Analysis, Institute of Applied Mathematics and Mechanics.

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Publications

1. Kovalevsky A.A., Gorban Yu.S. On Т-solutions of degenerate anisotropic elliptic variational inequalities with L^1-data. (Russian) Izv. Ross. Akad. Nauk Ser. Mat. 75 (2011), no. 1, 101-160; translation in Izv. Math. 75 (2011), no. 1, 101-156.
    
2. Kovalevsky A.A., Nicolosi F. On limit summability of solutions for a class of degenerate nonlinear high-order equations with L^1-data. Complex Var. Elliptic Equ. 55 (2010), no. 11, 1047-1058.
    
3. Kovalevsky A.A., Skrypnik I.I., Shishkov A.E. Singular solutions of nonlinear elliptic and parabolic equations. Naukova Dumka, Kyiv, 2010, 499 p. (Russian)
    
    
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4. Kovalevsky A.A., Rudakova O.A. Г-convergence of integral functionals with degenerate integrands in periodically perforated domains. Tr. Inst. Prikl. Mat. Mekh. NAN Ukrainy 19 (2009), 101-109.
    
5. Kovalevsky, A.A., Rudakova, O.A. Variational problems with pointwise constraints and degeneration in variable domains. Differ. Equ. Appl. 1 (2009), no. 4, 517-559.
    
    
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6. Kovalevsky A.A. Nonlinear fourth-order equations with a strengthened ellipticity and L^1-data. Alvino, A. (ed.) et al., On the notions of solution to nonlinear elliptic problems: results and developments. Caserta: Dipartimento di Matematica, Seconda Universita di Napoli; Rome: Aracne. Quaderni di Matematica, 23, 2008, 283-337.
    
7. Kovalevsky, A. A., Nicolosi, F. On multipliers characterizing summability of solutions for a class of degenerate nonlinear high-order equations with L^1-data. Nonlinear Anal. 69 (2008), no. 3, 931-939.
    
8. Kovalevsky, A.A., Nicolosi, F. On the sets of L^\infty-regularity of solutions for a class of degenerate nonlinear problems with slightly regular data. Nonlinear Anal. 68 (2008), no. 10, 3175-3185.
    
9. Kovalevsky, A.A., Nicolosi, F. On the sets of boundedness of solutions to degenerate fourth-order equations with strengtheningly monotone principal parts, absorption and L^1-data. Matematiche (Catania) 62 (2007), no. 2, 235-253.
    
10. Kovalevsky, A.A., Gorban, Yu.S. Degenerate anisotropic variational inequalities with L^1- data. C. R. Math. Acad. Sci. Paris 345 (2007), no. 8, 441-444.
     
11. Kovalevskiĭ, A.A., Nikolozi, F. On the sets of boundedness of solutions for a class of fourth-order degenerate nonlinear elliptic equations with L^1-data. (Russian) Fundam. Prikl. Mat. 12 (2006), no. 4, 99-112; translation in J. Math. Sci. (N. Y.) 150 (2008), no. 5, 2358-2368.
     
     
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12. Kovalevskiĭ, A.A., Voĭtovich, M.V. On increasing the summability of generalized solutions of the Dirichlet problem for fourth-order nonlinear equations with strengthened ellipticity. (Russian) Ukraïn. Mat. Zh. 58 (2006), no. 11, 1511-1524; translation in Ukrainian Math. J. 58 (2006), no. 11, 1717-1733.
     
13. Kovalevskiĭ, A.A. A priori properties of solutions of nonlinear equations with degenerate coercivity and L^1-data. (Russian) Sovrem. Mat. Fundam. Napravl. 16 (2006), 47-67; translation in J. Math. Sci. (N. Y.) 149 (2008), no. 5, 1517-1538.
     
     
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14. Kovalevsky, A., Nicolosi, F. On improvement of summability properties of solutions of some degenerate nonlinear fourth-order equations. Appl. Anal. 85 (2006), no. 10, 1207-1217.
     
15. Kovalevskiĭ, A.A., Rudakova, O.A. On the strong connectedness of weighted Sobolev spaces and the compactness of sequences of their elements. (Russian) Tr. Inst. Prikl. Mat. Mekh. NAN Ukrainy 12 (2006), 85-99.
     
16. Kovalevskiĭ, A.A. On the convergence of functions in a Sobolev space satisfying special integral estimates. (Russian) Ukraïn. Mat. Zh. 58 (2006), no. 2, 168-183; translation in Ukrainian Math. J. 58 (2006), no. 2, 189-205.
     
17. Kovalevsky, A.A. General conditions for limit summability of solutions of nonlinear elliptic equations with L^1-data. Nonlinear Anal. 64 (2006), no. 8, 1885-1895.
     
18. Kovalevsky A.A. Improvement of summability of entropy solutions for a class of nonlinear high-order equations. Nonlinear Analysis: Works of Ukrainian Mathematical Congress-2001. Inst. Mat. NAN Ukrainy, Kyiv, 2005, 42-49.
     
19. Kovalevskiĭ, A. A. On a sharp condition for the limit summability of solutions of nonlinear elliptic equations with L^1-right-hand sides. (Russian) Ukr. Mat. Visn. 2 (2005), no. 4, 502-540; translation in Ukr. Math. Bull. 2 (2005), no. 4, 507-545.
     
     
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20. Kovalevsky, A.A. The Dirichlet problem for nonlinear equations with degenerate coercivity and L^1-data. Tr. Inst. Prikl. Mat. Mekh. NAN Ukrainy 10 (2005), 72-78.
     
21. Kovalevsky A.A., Rudakova O.A. On Г-compactness of integral functionals with degenerate integrands. (Russian) Nelinejnye Granichnye Zadachi 15 (2005), 149-153.
     
22. Kovalevsky, A., Nicolosi, F. Existence and regularity of solutions to a system of degenerate nonlinear fourth-order equations. Nonlinear Anal. 61 (2005), no. 3, 281-307.
     
23. Kovalevsky, A., Nicolosi, F. Summability of solutions of some degenerate nonlinear elliptic fourth-order equations. Appl. Anal. 84 (2005), no. 1, 1-13.
     
24. Kovalevsky, A., Nicolosi, F. Solvability of Dirichlet problem for a class of degenerate anisotropic equations with L^1-right-hand sides. Nonlinear Anal. 59 (2004), no. 3, 347-370.
     
25. Kovalevskiĭ, A.A. Summability of solutions of nonlinear elliptic equations with right-hand sides in logarithmic classes. (Russian) Mat. Zametki 74 (2003), no. 5, 676-685; translation in Math. Notes 74 (2003), no. 5-6, 637-646.
     
     
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26. Kovalevskiĭ, A.A. On the summability of entropy solutions of the Dirichlet problem for a class of fourth-order nonlinear elliptic equations. (Russian) Izv. Ross. Akad. Nauk Ser. Mat. 67 (2003), no. 5, 35-48; translation in Izv. Math. 67 (2003), no. 5, 881-894.
     
     
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27. Kovalevsky, A., Nicolosi, F. Summability of solutions of Dirichlet problem for a class of degenerate nonlinear high-order equations. Appl. Anal. 82 (2003), no. 2, 93-101.
     
28. Kovalevsky, A., Nicolosi, F. Summability of solutions of Dirichlet problem. Acoustics, mechanics, and the related topics of mathematical analysis, 199-206, World Sci. Publ., River Edge, NJ, 2002.
     
29. Kovalevsky, A., Nicolosi, F. Existence of solutions of some degenerate nonlinear elliptic fourth-order equations with L^1-data. Appl. Anal. 81 (2002), no. 4, 905-914.
     
30. Kovalevsky A.A. Entropy solutions of Dirichlet problem for a class of nonlinear elliptic high-order equations with L^1-data. Nelinejnye Granichnye Zadachi 12 (2002), 119-127.
     
31. Kovalevsky, A., Nicolosi, F. Entropy solutions of Dirichlet problem for a class of degenerate anisotropic fourth-order equations with L^1-right-hand sides. Nonlinear Anal. Ser. A: Theory Methods 50 (2002), no. 5, 581-619.
     
32. Kovalevsky, A., Nicolosi, F. On the convergence of solutions of degenerate nonlinear elliptic high order equations. Nonlinear Anal. Ser. A: Theory Methods 49 (2002), no. 3, 335-360.
     
33. Kovalevskiĭ, A. A. On the integrability of solutions of nonlinear elliptic equations with right-hand sides in classes close to L^1. (Russian) Mat. Zametki 70 (2001), no. 3, 375-385; translation in Math. Notes 70 (2001), no. 3-4, 337-346.
     
     
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34. Kovalevsky, A., Nicolosi, F. Solvability of Dirichlet problem for a class of degenerate nonlinear high-order equations with L^1-data. Nonlinear Anal. 47 (2001), no. 1, 435-446.
     
35. Kovalevskiĭ, A. A. Entropy solutions of the Dirichlet problem for a class of fourth-order nonlinear elliptic equations with L^1-right-hand sides. (Russian) Izv. Ross. Akad. Nauk Ser. Mat. 65 (2001), no. 2, 27-80; translation in Izv. Math. 65 (2001), no. 2, 231-283.
     
     
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36. Kovalevsky, A., Nicolosi, F. On Hölder continuity of solutions of equations and variational inequalities with degenerate nonlinear elliptic high order operators. Current problems of analysis and mathematical physics (Italian) (Taormina, 1998), 205-220, Aracne, Rome, 2000.
     
37. Kovalevskiĭ, A.A. On the convergence of some numerical characteristics of Dirichlet variational problems in variable domains. (Russian) Ukraïn. Mat. Zh. 52 (2000), no. 11, 1497-1512; translation in Ukrainian Math. J. 52 (2000), no. 11, 1706-1723.
     
38. Kovalevskiĭ, A.A. Averaging of integral functionals associated with domains of periodic structure of framework type with thin channels. (Russian) Ukraïn. Mat. Zh. 52 (2000), no. 5, 616-625; translation in Ukrainian Math. J. 52 (2000), no. 5, 703-714.
     
     
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39. Kovalevsky, A., Nicolosi, F. On regularity up to the boundary of solutions to degenerate nonlinear elliptic high-order equations. Nonlinear Anal. Ser. A: Theory Methods 40 (2000), no. 1-8, 365-379.
     
40. Kovalevskiĭ, A.A. On a necessary condition for the strong G-convergence of nonlinear operators for the Dirichlet problem with variable domain. (Russian) Differ. Uravn. 36 (2000), no. 4, 537-541; translation in Differ. Equ. 36 (2000), no. 4, 599-604.
     
41. Kovalevsky, A., Nicolosi, F. Integral estimates for solutions of some degenerate local variational inequalities. Appl. Anal. 73 (1999), no. 3-4, 425-447.
     
42. Kovalevsky, A. An effect of double homogenization for Dirichlet problems in variable domains of general structure. C. R. Acad. Sci. Paris Sér. I Math. 328 (1999), no. 12, 1151-1156.
     
43. Kovalevsky A. Entropy solutions of Dirichlet problem for a class of nonlinear elliptic fourth order equations with L^1-data. Nonlinear Boundary Value Problems 9 (1999), 46-54.
     
44. Kovalevsky, A., Nicolosi, F. A weighted interpolation inequality of the Nirenberg-Gagliardo kind. Nonlinear Anal. Ser. A: Theory Methods 36 (1999), no. 3, 269-273.
     
45. Kovalevsky, A., Nicolosi, F. Boundedness of solutions of degenerate nonlinear elliptic variational inequalities. Nonlinear Anal. Ser. B: Real World Applications 35 (1999), no. 8, 987-999.
     
46. Kovalevsky, A., Nicolosi, F. Boundedness of solutions of variational inequalities with nonlinear degenerated elliptic operators of high order. Appl. Anal. 65 (1997), no. 3-4, 225-249.
     
47. Kovalevsky, A.A. On strong G-convergence of nonlinear elliptic high order operators corresponding to Dirichlet problems in variable domains. Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki 1997, no. 6, 27-30.
     
48. Kovalevsky, A.A. G-compactness of a sequence of nonlinear elliptic high order operators corresponding to Neumann problems in variable domains. Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki 1997, no. 5, 21-24.
     
49. Kovalevskiĭ, A.A. Γ-convergence of integral functionals and the Dirichlet variational problem in variable domains. (Russian) Ukraïn. Mat. Zh. 48 (1996), no. 9, 1236-1254; translation in Ukrainian Math. J. 48 (1996), no. 9, 1402-1422.
     
50. Kovalevskiĭ, A.A. On the Γ-convergence of integral functionals defined on weakly connected Sobolev spaces. (Russian) Ukraïn. Mat. Zh. 48 (1996), no. 5, 614-628; translation in Ukrainian Math. J. 48 (1996), no. 5, 683-698.
     
51. Kovalevskiĭ, A.A. G-compactness of sequences of nonlinear operators of Dirichlet problems with a variable domain. (Russian) Izv. Ross. Akad. Nauk Ser. Mat. 60 (1996), no. 1, 133-164; translation in Izv. Math. 60 (1996), no. 1, 137-168.
     
52. Kovalevsky A.A. Asymptotics of solutions of nonlinear Neumann problems in domains with accumulators. (Russian) Nelinejnye Granichnye Zadachi 6 (1995), 54-58.
     
53. Kovalevskiĭ, A.A. Homogenization of Neumann problems for nonlinear elliptic equations in domains with accumulators. (Russian) Ukraïn. Mat. Zh. 47 (1995), no. 2, 194-212; translation in Ukrainian Math. J. 47 (1995), no. 2, 227-249.
     
54. Kovalevsky, A.A. On the structure of G-limit operator for a sequence of nonlinear operators of Dirichlet problem with varying domain of definition. Dopov./Dokl. Akad. Nauk Ukraïni 1994, no. 12, 15-18.
     
55. Kovalevskiĭ, A.A. On the uniform boundedness of solutions of nonlinear elliptic variational inequalities in variable domains. (Russian) Differ. Uravn. 30 (1994), no. 8, 1370-1373; translation in Differ. Equ. 30 (1994), no. 8, 1270-1273.
     
56. Kovalevskiĭ, A.A. G-convergence and averaging of nonlinear elliptic operators in divergence form with a variable domain. (Russian) Izv. Ross. Akad. Nauk Ser. Mat. 58 (1994), no. 3, 3-35; translation in Russian Acad. Sci. Izv. Math. 44 (1995), no. 3, 431-460.
     
     
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57. Kovalevskiĭ, A.A. Averaging of Neumann problems for nonlinear elliptic equations in domains of framework type with thin channels. (Russian) Ukraïn. Mat. Zh. 45 (1993), no. 11, 1503-1513; translation in Ukrainian Math. J. 45 (1993), no. 11, 1690-1702.
     
58. Kovalevsky A.A. On a necessary condition of Г-convergence of integral functionals on sets of functions with restriction on the gradient. (Russian) Nelinejnye Granichnye Zadachi 5 (1993), 49-53.
     
59. Kovalevsky A.A. G-convergence of nonlinear problems in perforated domains. (Russian) Uspekhi Mat. Nauk 48 (1993), no. 4, 213-214.
     
60. Kovalevskiĭ, A.A. On the G-convergence of nonlinear elliptic operators associated with the Dirichlet problem in variable domains. (Russian) Ukraïn. Mat. Zh. 45 (1993), no. 7, 948-962; translation in Ukrainian Math. J. 45 (1993), no. 7, 1049-1065.
     
61. Kovalevsky, A.A. On G-convergence of operators of Dirichlet problem with varying domain. Dopov./Dokl. Akad. Nauk Ukraïni 1993, no. 5, 13-17.
     
62. Kovalevsky A.A. On necessary and sufficient conditions of Г-convergence of integral functionals with different domains of definition. (Russian) Nelinejnye Granichnye Zadachi 4 (1992), 29-39.
     
63. Kovalevskiĭ, A.A. Γ-convergence of integral functionals connected with the variational Dirichlet problem in variable domains. (Russian) Dokl. Akad. Nauk Ukrainy 1992, no. 12, 5-9.
     
64. Kovalevskiĭ, A.A. Convergence of solutions of variational inequalities with two-sided obstacles in punctured domains. (Russian) Ukraïn. Mat. Zh. 44 (1992), no. 2, 191-197; translation in Ukrainian Math. J. 44 (1992), no. 2, 170-175.
     
65. Kovalevskiĭ, A.A. G-convergence of abstract operators defined on weakly connected spaces. (Russian) Dokl. Akad. Nauk Ukrain. SSR 1991, no. 9, 27-30.
     
66. Kovalevsky A.A. On G-convergence of nonlinear elliptic operators with different domains of definition. (Russian) Nelinejnye Granichnye Zadachi 3 (1991), 26-35.
     
67. Kovalevskiĭ, A.A. Conditions for Γ-convergence and homogenization of integral functionals with different domains. (Russian) Dokl. Akad. Nauk Ukrain. SSR 1991, no. 4, 5-8.
     
68. Kovalevskiĭ, A.A. Necessary conditions for Γ-convergence of integral functionals. (Russian) Mat. Fiz. Nelineĭn. Mekh. 14 (1990), 68-71.
     
69. Kovalevskiĭ, A.A. Strong G-convergence of nonlinear elliptic operators connected with punctured domains. (Russian) Dokl. Akad. Nauk Ukrain. SSR Ser. A 1990, no. 7, 14-17.
     
70. Kovalevskiĭ, A.A. Some problems connected with the problem of averaging variational problems for functionals with a variable domain. (Russian) Current analysis and its applications (Russian), 62-70, Naukova Dumka, Kiev, 1989.
     
71. Kovalevsky A.A. On connectedness of subsets of Sobolev spaces and Г-convergence of functionals with varying domain of definition. (Russian) Nelinejnye Granichnye Zadachi 1 (1989), 48-54.
     
72. Kovalevskiĭ, A.A. G-convergence of operators defined on various Banach spaces, and the convergence of solutions of variational inequalities. (Russian) Dokl. Akad. Nauk Ukrain. SSR Ser. A 1989, no. 5, 15-17.
     
73. Kovalevskiĭ, A.A. G-convergence of abstract operators with different domains. (Russian) Dokl. Akad. Nauk Ukrain. SSR Ser. A 1989, no. 3, 20-23.
     
74. Kovalevskiĭ, A.A. Averaging of variable variational problems. (Russian) Dokl. Akad. Nauk Ukrain. SSR Ser. A 1988, no. 8, 6-9.
     
75. Kovalevskiĭ, A.A. Asymptotic behavior of solutions of the second boundary value problem for quasilinear elliptic equations in domains with a fine-grained boundary. (Russian) Mat. Fiz. Nelineĭn. Mekh. 2 (1984), 50-53.