Arkhipova  A.A.

 

RESEARCH  PUBLICATIONS:

  
Book:

    The regularity of Week Solutions of Boundary-Value Problems to Linear Elliptic Equations and Systems of Equations. Textbook. St - Petersburg State Univ.1998, 
    103 pp.

Research articles:

  1. On the supersolutions to the obstacle problem.//Izvestiya Akad. Nauk SSSR, 37 (5), 1973, pp.1155-1185.
  2. On the smoothness of the solutions of the obstacle problem. //Zapiski Nauchn. Semin. LOMI, 38, 1973, pp.7-9.
  3. Discontinuous obstacle problem for uniformly elliptic equations.//Vestnik Leningrad Univ. Ser. Math., 19, 1974, pp. 154-155.
  4. The Obstacle problem to some classes of quasilinear elliptic equations. //Problemy Math. Analysis, Leningrad Univ., math. 5, 1976, pp. 3-24.
  5. Variational problem for some degenerative functional.// Problemy Math. Analysis, Leningrad Univ., math. 6, 1977,  pp.10-18.
  6. On the smoothness of the Dirichlet problem for nonunimformly elliptic equations. //Problemy Math. Analysis, 7, 1979, pp. 3-13.
  7. On the properties of weak solutions of the Euler  equations of some class of nonsmooth functionals. //Izvestiya VUZov, ser. Math. 11, 1982, pp. 5-9.
  8. On the smoothness of a solution of some system of variational inequalities. //Vestnik Leningrad Univ., ser. Math. 7, 1982, pp. 48-52.
  9. On the best possible smoothness of the problem with two-sided constraints. //Vestnik Leningrad Univ., ser. Math., 7, 1984, pp. 5-9.
  10. On the best possible smoothness of the solution of  nonstationary one or two obstacles problem.// Problemy Math. Analysis, Leningrad Univ., math. 9, 1984, pp.149-156.
  11. Regularity of the solution of some system of variational inequalities with a constrain in Rn.// Vestnik Leningrad Univ., ser. math., 13, 1984, pp. 5-9.
  12. On the solution of weak- connected parabolic system with one-side boundary constrain.// Vestnic Leningrad Univ. ser. math. 11, 1987, pp. 3-6.
  13. Regularity of the solutions of some diagonal elliptic systems of variational inequalities.// Problemy Math. Analysis, Leningrad Univ., math. 10, 1986, pp. 3-16.
  14. Two- sided boundary contraints  problem// Proceedings of the Operator Theory Summer School, X. (Thesis of the lecture). Donetsk, Academy of Science of the USSR, 1986.
  15. Regularity of solutions of a problem with two-sided constraints on a boundary for elliptic and parabolic equations (with Uraltseva N.N.).// Proc. Steklov Inst. Math. 2, 1989, pp. 1-19 ( In Russian: Trudy MIAN, 179, 1987, pp. 5-22).
  16. On the regularity of solutions of the problem with two- sided boundary constraints (with Uraltseva N.N.). //Vestnik Leningrad Univ. Math. 19 (1), 1986, pp. 3-9.
  17. The regularity of solutions of diagonal elliptic systems under convex boundary constraints ( with Uraltseva N.N.). //Journal  the Soviet Math. 40 (5), 1988, pp. 591-599 (in Russian: Zapiski Nauchn. Semin. LOMI, 18, 1986, pp. 5-17).
  18. The regularity of solutions of variational inequalities with convex boundary constraints for nonlinear operators with diagonal mail part(with Uraltseva N.N). //Vestnik Leningrad Univ. Math. 15, 1987, pp. 13-19.
  19. The best possible smoothness for solutions of variational inequalities with convex boundary constraints (with Uraltseva N.N).//Journal of Soviet Math. 49 (5), 1990, pp. 1121-1128 (In Russian: Zapiski nauchn. Semin. LOMI, 19, 1987, pp. 5-16).
  20. The problem with convex boundary consraints (with Uraltseva N.N). //Uspekhi Math. Nauk 42 (4), 1987.
  21. On the smoothness of the solution of the Dirichler problem for nonuniformly elliptic equations.// Sel. Math. Sol. 5 (2), 1986, pp. 127-136.
  22. On the reqularity of the solutions of the variational inequalities. //Proceedings of the Operator Theory School, XIII. Thesis of the lecture. Kujbyshev, Academy of Science of the USSR.1988.
  23. On the regularity of the solution of the obstacle up to the boundary problem for strong elliptic operators. //Some Applications Func.Analysis to Math. Physics Problems. Novosibirsk, SO AN SSSR, 1988, pp. 3-20.
  24. On the second derivatives of the solutions of some variational inequalities introduced by elliptic nondiagonal systems.// Problemy Math. Analysis, Leningrad Univ., Math. 11, 1990, pp. 6-17.
  25. On the existence of smooth solutions of problems with convex constraints on the boundary to parabolic systems (with Uraltseva N.N). //Journal of Soviet Math. 56 (2), 1991, pp. 2281-2285. (In Russian: Zapiski Nauchn.Semin. LOMI, 20, 1989, pp.3-9).
  26. Holder norm estimate for approximations of the boundary constraint problem to diagonal parabolic system.// Vestnik Leningr. Univ. ser. Math. Depon. VINITI  № 1149- B89, 21.02.89, 1989.
  27. The application of the reverse Holder inequalities to investigation of the regularity of of solutions of elliptic and parabolic systems.// Proceedings of the Conference on the PDEs, Frunze, USSR, 1989. Thesis of the lecture.
  28. Reverse Holder inequalities with the boundary integrals and  L-p estimates in the Neumann problems.// Embedding Theorems Applications to Math Physics Problems. Novosibirsk, SO AN SSSR, 1989, pp.3-17.
  29. Reverse Holder Inequalities in Parabolic Initial- Boundary Problems.// Proceedings of the Operator Theory School, XV. Thesis of the lecture. Ul’anovsk, Academy of Science of the USSR, 1990.
  30. Some applications of the reverse Holder inequalities with the boundary integrals. //Problemy J. Math. Sci. 72 (6), 1994  (In Russian: Problemy Math. Analysis. Petersburg Univ. 12, 1992, pp. 13-29.
  31. L-p estimates of the gradients of the solutions of the initial- boundary problems to quasilinear parabolic systems.//J .of  Math. Sciences, 73 (6), 1995, pp. 609 - 617 (In Russian: Problemy Math. Analysis, Petersburg Univ., Math. 13, 1992, pp. 5-18).
  32. Partial regularity of the solutions of quasilinear elliptic systems with nonsmooth Neumann-type boundary condition.// Russian Acad. Sci. Sb. Math. 78 (1), 1994, pp. 215-230 ( In Russian: Matematich. Sbornyk, 184 (2), 1993 ).
  33. Reverse Holder Inequalities in parabolic problems with anisotropic data. //Trudy Inst. Of Math. SO RAN, 24, 1994, pp.3-19.
  34. On the regularity of solutions of the oblique derivative problem for quasilinear elliptic systems. //Zapiski Nauchn.Semin. POMI, 213, 1994, pp. 1-8.
  35. Regularity of the solutions of quasilinear elliptic systems under nonlinear boundary condition. //J.Math.Sci, 77 (4), 1995, pp.3277-3294 (In Russian: Problemy Math. Analysis, Petersburg Univ. 14, 1995, pp. 3-28).
  36. Reverse Holder inequalities with boundary integrals and L-p - estimates for solutions of elliptic and parabolic nonlinear boundary - value problems. //Preprint 93- 123, CWRU, Cleveland, USA, 1993.
  37. On the Neumann problem for quasilinear parabolic systems under  controllable growth  conditions. I. L-p - regularity results.// Preprint 93 - 127 CWRU, Cleveland, USA, 1993.
  38. On the Neumann problem for quasilinear parabolic systems under controliable growth conditions. II. Partial Holder continuity of solutions.// Preprint 93-128, CWRU. Cleveland, USA. 1993.
  39. On the Regularity of the Oblique Derivative Problem to Quasilinear Elliptic Systems. //Preprint 93-131, CWRU. Cleveland, USA. 1993.
  40. Mathematical Physics Methods. Program and  methodical instructions. State Russian  Committee of High Education.// Program < Universities of Russia>, F.00.01 Math. SPbGU, 2, 1995.
  41. On the regularity of the solutions of the Neumann problem for quasilinear parabolic systems.// Russian Acad. Sci. Izv. Math. 45 (2), 1995, pp. 231-253 ( In Russian: Izvestiya Ross. Akad. Nauk, ser. Math. 58, 1994, pp. 3-25).
  42. On the regularity of the solutions of some model nonlinear elliptic systems under oblique derivative type boundary condition.// Zapiski Nauchn. Semin. POMI, 221, 1995, pp. 30-57.
  43. On the regularity of solutions of boundary-value problem for quasilinear elliptic systems with quadratic nonlinearities. //J. Math. Sci. 80 (6), 1996, pp. 2208-2225 (In Russian: Problemy  Math. Analysis, Petersburg Univ. math. 15, 1995).
  44. Reverse Holder inequalities with boundary integrals and L-p estimates for solutions of elliptic and parabolic nonlinear boundary - value problems. //Amer. Math. Soc. Transl. 164 (2), 1995.
  45. On the Neumann problem for nonlinear elliptic systems with quadratic nonlinearity. //St. Petersburg Math.J. 8 (5), 1997, pp. 1-17 ( In Russian: Algebra & Analysis, St-Petersburg  8 (5), 1996 ).
  46. Global solvability for nondiagonal parabolic systems of  variational structure in the case of two spatial variables..// Problemy Math. Analysis, Petersburg Univ. Math. 16, 1996, pp. 3-40.
  47. Sharp estimates for Solutions of a parabolic Signorini problem (with Uraltseva N.N.).// Math. Nachr. 177, 1996.
  48. On the initial boundary- value problems for nondiagonal quasilinear parabolic systems with quadratic nonlinearities.// International Conference Nonlinear PDE, Kiev, 1997. Books of Abstracts.
  49. On the partial regularity up to the boundary of weak solutions to quasilinear parabolic systems with quadratic growth. //Zapiski Nauchn. Semin. POMI, 249, 1997, pp.20-39.
  50. On some modifications of Gehring Lemma arising from the investigation of parabolic boundary -value problems.// Problemy Math. Analysis. Petersburg Univ., Math. 17, 1997, 1997, pp. 20-45.
  51. Partial regularity of weak solutions of nonlinear boundary- value problems for elliptic and parabolic systems of the second order. //Avtoreferat of the doctoral thesis. St-Petersburg state Univ., 1997.
  52. On the global in time solvability of the Cauchy - Diriclet Problem to nondiagonal parabolic systems with quadratic nonlinearities.// International Conference PDE Prague’98. Book of Abstract, p. 42.
  53. On the solvability problem for one class of nondiagonal  parabolic systems with quadratic nonlinearites.  (thesises)//   International conference NPDE’99. L’viv,
    August 23-29,1999.  Book of Abstracts, p.8.
  54. Методы математической физики. Учебная программа с методическими указаниями для студентов математико-механического факультета,
    специальности: механика, прикладная механика. //  Гос.Комитет России по Высшему Образованию. Программа Университеты России. СпбГУ, вып.2, с.15-22, 1996. (Thesises of lectures on Mathematical Physics for students of Mathematical  Faculties.  Program “ Universities of  Russia”.)
  55. Regularity of weak solutions of  boundary-value problems for linear equations. (for students).// St-Petersburg  State Univ., 1998, 101 pp.
  56. Introduction in Functional Analysis.( book for students). // St-Petersburg State University, 1999, 50 pp.
  57. Local and global in time solvability of the Cauchy-Dirichlet problem for a class of  nonlinear nondiagonal parabolic systems. // Algebra & Analysis,
    St-Petersburg, Russia v.6, (1999), 81-119.  in English:  St-Petersburg Math.J., v.6 (2000).
  58. Cauchy-Neumann problem to a class of nondiagonal parabolic systems with quadratic growth nonlinearities. I.Continuability of smooth solutions. // CMUC, v.41, (4),  (2000), 693-718.
  59. Cauchy-Neumann problem to a class of nondiagonal parabolic systems with quadratic growth nonlinearities . II. Local and Global Solvabiliry Results.
      // CMUC,  v.42  (1),   (2001),  53-76.
  60. Partial regularity  up to the boundary of weak solutions of elliptic systems with nonlinearity  q  greater  than two.//  Zapiski Nauchn. Seminarov  POMI,
          v.271, (2000),  63-82. 
  61. On the classical solvability of Cauchy-Dirichlet problem for  two-dimensional  nondiagonal  parabolic systems .//  Trudy St-Petersburg Mathematical Society.
    V.9,  (2001),  3-22.
  62. Solvability problem for strongly nonlinear nondiagonal parabolic systems.//  Math. Bohemica, v. 127  (2002), n..2,  -- Proceedings of Equadiff-10.
  63. Continuability in time of smooth solutions of strong-nonlinear non-diagonal   parabolic   systems.// Ann.Scuola Norm. Sup.Pisa,  Cl. Sci. (5), v.1,  (2002),  153-167.
  64. On the global solvability  of the Cauchy-Dirichlet problem  for a class of  nondiagonal   parabolic systems with q-nonlineariry on the gradient, 1<q<2.   // Zapiski POMI, v.288,  (2002),  34-78.  in English:  J. Math Sci., v.123 (6),  (2004),  4539-45-83.
  65. Solvability problem  for nondiagonal elliptic systems with quadratic nonlinearity on the gradient. (the two-dimensional case).  // Zapiski POMI, v.295,  (2003), 5-17.
  66. Regularity of  solutions of the diffraction-type problem for linear elliptic systems in the Campanato spaces. (with Osman Ell Homahmi) // Problemy Matem.      Analiza,  (Tamara Rozhkovskaya,  Novosibirsk),   v..24,  (2002),  29-60.
  67. Quasireverse Holder inequalities and a priori estimates for quasilinear elliptic systems. //  Rendic. Mat. Acc. Lincei,  s.9, v. 14, (2003),  91-108.
  68. Boundary a priori estimates for solutions of nondiagonal elliptic systems with strong nonlinearity. // Izvestija RAN,  ser mat., v.68, n. 2,  (2004),  23-38 .
  69. New a priori estimates for q- nonlinear elliptic systems with strong nonlinearities in  the gradient,   1<q<2.  // Zapiski  Nauchn. Semin. POMI, v.310, (2004),  19-48.
  70. On the smoothness of weak solutions of strong- nonlinear nondiagonal elliptic systems  (the two-dimensional case). //Zapiski  Nauchn. Semin. POMI.  V.318, (2004),  5-13.
  71. Nina Nikolaevna Uraltseva. To 70-th birthday.   (with Seregin G.A.) // Zapiski Nauchn. Semin. POMI, v.310,  (2004), 7-18.
  72. Quasireverse Holder inequalities in parabolic metric and their applications.// AMS Translations  (Advances in Math. Sci.,  v.220,  (2007), 1-26.
  73. Monotonicity   condition and a priori estimates of  the Holder norm  for class  of nondiagonal  elliptic systems with quadratic nonlinearity. //  Problemy      Matem. Analiza, v.34,  (2006),  11-22.  in  english: J. Math. Sci.,  v.142, n.1, (2007), 1733-1748.
  74. New a priori estimates for nondiagonal strongly nonlinear parabolic systems. // Banach Center Publications, Warszawa, v. 86, (2008), 3-27, (Proceedings of the conference “Parabolic  and Navier-Stokes equations”, 2006,  September,  Bedlewo).
  75. Variational problem with an obstacle in R^N for a class of quadratic functionals // Zapiski  Nauchn. Semin. POMI, т.362, с.1-32, 2008.
  76. Signorini problem in R^N for a class of quadratic functionals // Amer. Math Soc. Transl., ser.2, v.229,  15-38, 2010.
  77. A priori estimates for quasilinear parabolic systems with quadratic nonlinearitiesinthe gradient  (with J. Stara) //  Comment. Math. Univ. Carolin., v.51, 2-16, 2010.
  78. Задача с препятствием, выходящим на границу области для некоторого класса квадратичных функционалов в R^N.  // Алгебра и Анализ, т.22, (6), 3-42,  2010.
  79. Heat flows for a nonconvex Signorini type problem in R^N. // Problemy Matem.Analiza, (Tamara Rozhkovskaya,  Novosibirsk), 58, 25-46,  2011.