Professor Victor Burenkov

Pure Mathematics

(real and functional analysis, especially theory offunction spaces (Sobolev spaces, spaces with fractional order of smoothness),partial differential equations, especially theory of hypoelliptic equations andectral theory (spectral stability estimates for eigenvalues and eigenfunctions of elliptic operators), integral equations, especially ill-posed problems.

Applied Mathematics

(applications to geophysics, quantum mechanics, numerical methods, radars).

Current research interests

Topics: Integral inequalities in general Morrey-type spaces, spectral stability of differential operators

Subtopics:

1. Compactness of the Riesz potential in general Morrey-type spaces
2. Boundedness and compactness of singular integral operators in general Morrey-type spaces.
3. An analogues of Young’s and O'Neil's inequalities for convolutions in general Morrey-type spaces.
4. Inequalities for entire functions of exponential type in general Morreytype spaces.
5. Application of conformal mappings to obtaining spectral stability estimates for the Dirichlet and Neumann Laplacians.
6. Spectral stability of the Schrodinger operator.

Moscow institute of physics and technology , Moscow institute of radio engineering, electronics and automation, Peoples' Friendship University of Russia (Russia), Cardiff University (UK), University of Padua (Italy), L.N. Gumilyov Eurasian National University (Kazakhstan)

Lecture courses on calculus, real analysis, complex analysis, functional analysis, integral equations, harmonic analysis, theory of distributions, partial differntial equations,  theory of function spaces, spectral theory.

Worked out the lecture course “The main ideas in the theory of Sobolev spaces” with flexible duration from 4 to 30 lectures, based on the book “Sobolev spaces on domains”, and delivered it in more than 10 universities around the world.

Postgraduate students

26 of them gained Ph.D.: Russia (8), Kazakhstan (6), Italy (2), Belarus (1), Syria (1), Togo (1), Nepal (1), Algeria (1), Ephiopia (1), Mexico (1), Colombia (1), Saudi Arabia (1), Azerbaijan (1)

• Burenkov V.I., Sobolev spaces on domains, B.G. Teubner, Stuttgart - Leipzig (1998), 312 pp
• Burenkov V. I., Iwaniec T., Vodopyanov S. K. (editors), The interaction of analysis and geometry. Contemporary Mathematics, v. 424. American Mathematical Society (2007)
• Burenkov V. I., M.L. Goldman, E.B. Laneev, V.D. Stepanov (editors). Progress in analysis. Proceedings of the 8th Congress of the International Society for analysis, its applications and computation (ISAAC), held in Moscow in August 2011. Vol. 1. Moscow, Peoples' Friendship University of Russia (2012). 511 pp. ISBN 978-5-209-04582-3.
• Burenkov V. I., M.L. Goldman, E.B. Laneev, V.D. Stepanov (editors). Progress in analysis. Proceedings of the 8th Congress of the International Society for analysis, its applications and computation (ISAAC), held in Moscow in August 2011. Vol. 2. Moscow, Peoples' Friendship University of Russia (2012). 335 pp. ISBN 978-5-209-04590-8.
• Burenkov V. I., S.S. Demidov, E.B. Laneev, S.A. Rozanova (editors). Progress in analysis. Proceedings of the 8th Congress of the International Society for analysis, its applications and computation (ISAAC), held in Moscow in August 2011. Vol. 1. Moscow, Peoples' Friendship University of Russia (2012), 276 pp. ISBN 978-5-209-04597-7.

Conferences

Gave invited talks at more than 100 international conferences in more than 30 countries.

Research Grants

• 2014- to present  Russian Science Foundation (project 14-01- 00443, Actual problems of the theory of spaces of differentiable functions and applications)
• 2014- to present  Russian Foundation for Basic Research (project 14-01- 00684, Spaces of differentialble functions of several variables and applications)
• 2014-to present Ministry od Science and Education of Kazakhstan (Fourier-Haar series, Fourier integrals and function spaces)
• 2013-2015 Ministry od Science and Education of Kazakhstan (project 1889 GF3  Investigation of stability of the main characteristics of differential operators upon domain perturbation), head of the  project
• 2012-2014 Ministry od Science and Education of Kazakhstan (project 1834 GF2 Operators in Morrey-type spaces and applications to partial differential equations), head of the  project
• 2012-2014 Peoples' Friendship University of Russia (project 020211-1-274) Functional and qualitative methods in the theory of differential equationsand interdisciplinary rerearch)
• 2012 - 2014 Russian Foundation for Basic Research (project 12-0100554-a, Integral inequalities and applications)
• 2011- 2013 Russian Foundation for Basic Research (project 11-0100744-a, Function spaces and applications)
• 2010 - 2011 Russian Foundation for Basic Research and DFG (Germany) (project 10-01-91331, Function spaces and applications to partial differential equations, spectral theory and fractal analysis)
• 2009 - 2011 Russian Foundation for Basic Research (project 09-01-00093a, Function spaces and applications)
• 2006 - 2009 INTAS, Function spaces and applications to partial differential equations (project 05 -100008-8157), head of the  project
• 2006 - 2008 Russian Foundation for Basic Research and DFG (Germany) (project 06-01-04006, Function spaces and applications to partial differential equations, spectral theory and fractal analysis), co-head of the  project
• 2005 - 2007 Russian Foundation for Basic Research, Inequalities for integral and differential operators and applications (project 05-01-04006 )
• 2001 - 2003 NATO Science Programme. Collaborative Linkage Grant UK-Azerbaijan, Weighted spaces of differentiable functions, weighted inequalities for integral operators and applications (project PST. CLG.978412),  co-head of the  project
• 2000 - 2002 INTAS, Function spaces and harmonic analysis (project 9901080)
• 2000 - 2001, 2001- 2002 Anglo-Portuguese Joint Research Programme (Treaty of Windsor), Fourier multipliers, potential-type operators and application, head of the  project
• 1999 - 2001 Russian Foundation for Basic Research, Sharp integral inequalities and applications (project 99-01-00843)
• 1995 - 1998 INTAS, Weighted inequalities (criteria, sharp constants) with applications to differential equations (project 94-881)
• 1996 - 1998 Russian Foundation for Basic Research (project 96-01-01380), head of the  project
• 1993 - 1995 Russian Foundation for Basic Research (project 93-01-00457), head of the  project

Editorial activities

• Member of the editorial boards of the journals ``Vestnik of Peoples' Friendship University. Mathematics" (through 1994-1998 editor- in-chief), ``Mathematical  Inequalities and Applications", ``Function Spaces and Applications", ``Journal of Inequalities in Pure and Applied Mathematics", ``ISAAC Monograph Series in Analysis, Applications and Computation".
• Editor-in-chief of the ``Eurasian Mathematical Journal" (together with M. Otelbaev and V.A. Sadovnichy)

Participation in international bodies

• Member of the London Mathematical Society
• International Society for Analysis, Applications and Computation (ISAAC), member, 1997 - to present, Vice-president 2003 – 2013.