Mатематический анализ

Миклюков Владимир Михайлович
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2010, ISBN 978-5-9669-0714-3
ББК 22.313.3я43 M59
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2010, ISBN 978-5-9669-0772-3
ББК 22.313.3я43 З-32
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On Almost Solutions of PDE
Preface in English.

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Dr. of Sci. (Math.) Prof. Vladimir M. Miklyukov.
Curriculum Vita

In 1968, Vladimir Miklyukov graduated from Donetsk State University (Ukraine) with a diploma in Mathemitics and started his postgraduate program under supervision of Academician Georgy D. Suvorov at Donetsk Computational Center (Ukraine, 1968-1970). The results of his work of that time pertained to the problem of removable singularities, problem of existence of angular boundary values, stability estimates of quasiconformal mappings of a ball onto a ball, and the problem of existence of quasiconformal mappings with unbounded characteristics. He defended his Ph.D. thesis Theory of Quasiconformal Mappings in Space in 1970 at Donetsk State University (Ukraine).

From 1970 to 1973, he was doing a research at the Institute of Applied Mathematics & Mechanics (Donetsk, Ukraine).

From 1973 to 1981, he continued his career working as a docent (associated professor) at Tyumen State University (Russia). While majoring in the field of quasiconformal mappings theory, he also got interested in strong nonlinear elliptic type PDE. The main publications of that time-frame were related to

  • the direct problem of holomorphic functions approximation theory for domains with quasiconformal boundary (with Vladimir I. Beliy);
  • the problem of boundary behaviour of minimal graphs;
  • estimates for extremal length of families of curves on minimal surfaces;
  • the Phragmen-Lindelöf and Ahlfors type theorems for quasiconformal mappings in space;
  • maximum principle for derivatives of solutions for minimal surfaces type equations;
  • Nitsche problem of minimal surfaces lying over-narrow in infinity domains.
In 1981 he defended his doctoral thesis Capacity Methods in the Problem of Nonlinear Analysis at Mathematical Institute of Ukrainian Academy of Sciences (Kiev, Ukraine).

In the same year, he became a full-time professor and a chairman of the department of Mathematical Analysis and Theory of Functions at Volgograd State University (Russia). His research interests concentrated on geometrical analysis. At the same time he was studying zero mean curvature surfaces in Euclidean and pseudoeuclidean spaces, nonlinear elliptic type PDE and quasiregular mappings of Riemannian manifolds. The main results of that work were related to the following groups of questions:

  • The external geometrical structure of zero mean curvature surfaces in Euclidean and pseudoeuclidean spaces; spacelike tubes and bands of zero mean curvature, their stability and instability with respect to small deformations, their life-time, branches, connections between branch points and Lorentz invariant characteristics of surfaces.
  • Phragmen-Lindelöf type theorems for differential forms; Ahlfors type theorems for differential forms with finite or infinite number of different asymptotic tracts; generalizations of Wiman theorem of forms, applications to quasiregular mappings on manifolds; applications of isoperimetric methods to the Phragmen-Lindelöf principle for quasiregular mappings on manifolds.

From July 1998 to July 2000, he was a visiting professor of Brigham Young University (USA).

In 2004, he focused his research on the mathematical theory of superslow processes and differential forms in micro- and nanocanals, and founded the Laboratory of Superslow Processes (Volgograd State University, Russia).

Vladimir M. Miklyukov is the author of more than 200 publications in Mathematics including the monographs:

  • Conformal Maps of Nonsmooth Surfaces and Their Applications;
  • Introduction to Nonsmooth Analysis;
  • Geometric Analysis: Differential Forms, Almost Solutions and Almost Quasiconformal Maps;
  • Tubes and Bands in Space-Time (with Vladimir A. Klyachin).

Learners of Vladimir Miklyukov are:

  • Doctor of Sci. (Math.) Prof. Victor I. Kruglikov (Tyumen State Univ.);
  • Victor I. Pelikh (Volgograd State Univ.), Ph.D.;
  • Vladimir A. Botvinnik (Volgograd State Univ.), Ph.D.;
  • Vladimir M. Keselman (Moscow Industr. Univ.), Ph.D.;
  • Aleksandr D. Vedenyapin (Volgograd State Univ.), Ph.D.;
  • Doctor of Sci. (Math.) Prof. Vladimir G. Tkachev (Volgograd State Univ.);
  • Doctor of Sci. (Math.) Prof. Aleksey A. Klyachin (Volgograd State Univ.);
  • Doctor of Sci. (Math.) Prof. Vladimir A. Klyachin (Volgograd State Univ.);
  • Natalia V. Loseva (Volzskiy Branch of Volgograd State Univ.), Ph.D.;
  • Repsime S. Akopyan (Volgograd Univ. of Consumer Cooperation), Ph.D.;
  • Aleksey V. Kochetov (Volgograd State Univ.), Ph.D.

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