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Personal data |
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Education and degrees |
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Experience in scientific institutes |
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Teaching experience |
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Research interests |
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Participation in scientific projects |
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Selected publications |
| Personal data: |
Last name: Parfenov
First name: Anton
Middle name: Igorevich
Data of birth: April 6, 1979 (Novosibirsk, Russia)
Languages: Russian (native), English, French
| Education and degrees: |
1995-2001 - Department of Mechanics and Mathematics, Novosibirsk State University (Novosibirsk).
2001 - Diploma, Novosibirsk State University (Novosibirsk).
2001-2002 - Master's degree programme, Department of Mechanics and Mathematics, Novosibirsk State University (Novosibirsk).
2002 - M. Sc., Novosibirsk State University (Novosibirsk).
2002-2005 - Postgraduate, Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences (Novosibirsk).
2005 - Candidate of Physical and Mathematical Sciences (Ph. D.), Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences (Novosibirsk).
Ph. D. Thesis "Riesz basis property of eigenfunctions of indefinite elliptic problems".
Ph. D. Advisor: Professor Sergei G. Pyatkov.
| Experience in scientific institutes: |
2002-2005 - Junior Scientific Researcher, Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences (Novosibirsk).
2005 - Leading Engineer, Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences (Novosibirsk).
2005-2006 - Scientific Researcher, Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences (Novosibirsk).
2006-present - Senior Scientific Researcher, Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences (Novosibirsk).
| Teaching experience: |
2004-2008 - Assistant Lecturer, Novosibirsk State University (Novosibirsk). ("Foundations of Functional Analysis")
| Research interests: |
Flattenability of domains with preservation of function spaces, elliptic boundary value problems
| Participation in scientific projects: |
Project "Spectral Theory of Operators in Indefinite Inner Product Spaces. Interpolation of Weighted Sobolev Spaces. Boundary Problems for Differential-Operator Equations ", supported by the Russian Foundation for Basic Research (RFBR), no. 03-01-00819 (2003-2005)
Project "Discrete Norm in Trace Spaces and its Applications", state scholarship for young Russian candidates of sciences (Ph.D.), no. 3099.2007.1 (2007-2008; head)
Project "Constructing and Studying Adequate Mathematical and Computer Models for Solving Problems of Biology, Continuum Mechanics, Semiconductor Physics – Analytical Methods and Computational Experiment", supported by the Ministry of Education and Science of the Russian Federation, Federal Target Program "Scientific and Educational Personnel of Innovative Russia'" for 2009-2013, contract no. 14.B37.21.0355, implemented work "Studying Asymptotic Behavior of a Harmonic Function near the Boundary" (2012-2013)
Project "Geometry and Mathematical Physics", state scholarship for leading scientific schools, no. 5913.2018.1 (2018-2019)
| Selected publications: |
Articles:
1. On an embedding criterion for interpolation spaces and application to indefinite spectral problems. Sib. Mat. Zh., 44 (2003), no. 4, pp. 810-819; English transl. in Sib. Math. J., 44 (2003), no. 4, pp. 638-644.
2. The Curgus condition in Sturm-Liouville problems. Mat. Tr., 7 (2004), no. 1, pp. 153-188; English transl. in Sib. Adv. Math., 15 (2005), no. 2, pp. 68-103.
3. On existence of a contraction mapping preserving boundary values. Vestnik NGU. Ser.: matematika, mekhanika, informatika. 7 (2007), iss. 2, pp. 70-92. (Russian)
4. A discrete norm on a Lipschitz surface and the Sobolev straightening of a boundary. Mat. Tr., 10 (2007), no. 2, pp. 163-186; English transl. in Sib. Adv. Math., 18 (2008), no. 4, pp. 258-274.
5. A criterion for straightening of a Lipschitz surface in the Lizorkin-Triebel sense. I. Mat. Tr., 12 (2009), no. 1, pp. 144-204; English transl. in Sib. Adv. Math., 20 (2010), no. 2, pp. 83-127.
6. A criterion for the straightening of a Lipschitz surface in the Lizorkin-Triebel sense. II. Mat. Tr., 12 (2009), no. 2, pp. 139-159; English transl. in Sib. Adv. Math., 20 (2010), no. 3, pp. 201-216.
7. A criterion for straightening a Lipschitz surface in the Lizorkin-Triebel sense. III. Mat. Tr., 13 (2010), no. 2, pp. 139-178; English transl. in Sib. Adv. Math., 21 (2011), no. 2, pp. 100-129.
8. A characterization of multipliers in the Hedberg-Netrusov spaces. Mat. Tr., 14 (2011), no. 1, pp. 158-194; English transl. in Sib. Adv. Math., 22 (2012), no. 1, pp. 13-40.
9. Weighted a priori estimate in straightenable domains of local Lyapunov-Dini type. Sib. Elektron. Mat. Izv., 9 (2012), pp. 65-150. (Russian)
10. Error bound for a generalized M.A. Lavrentiev’s formula via the norm in a fractional Sobolev space. Sib. Elektron. Mat. Izv., 10 (2013), pp. 335-377. (Russian)
11. Discrete Holder estimates for a parametrix variation. Mat. Tr., 17 (2014), no. 1, pp. 175-201; English transl. in Sib. Adv. Math., 25 (2015), no. 3, pp. 209-229.
12. Discrete Holder estimates for a certain kind of parametrix. II. Ufim. Math. J., 9 (2017), no. 2, pp. 63-93; English transl. in Ufa Math. J., 9 (2017), no. 2, pp. 62-91.
13. Series in a Lipschitz perturbation of the boundary for solving the Dirichlet problem. Mat. Tr., 20 (2017), no. 1, pp. 158-200; English transl. in Sib. Adv. Math., 27 (2017), no. 4, pp. 274-304.
14. Approximate calculation of the defect of a Lipschitz cylindrical condenser. Sib. Elektron. Mat. Izv., 15 (2018), pp. 906-926. (Russian)
15. Criterion for the vanishing of the oscillation of the real part of a conformal mapping of strips. Sib. Elektron. Mat. Izv., 16 (2019), pp. 1171-1195. (Russian)
16. Criterion for the Sobolev well-posedness of the Dirichlet problem for the Poisson equation in Lipschitz domains. I. Sib. Elektron. Mat. Izv., 17 (2020), pp. 2142-2189. (Russian)
17. Criterion for the Sobolev well-posedness of the Dirichlet problem for the Poisson equation in Lipschitz domains. II. Sib. Elektron. Mat. Izv., 20 (2023), no. 1, pp. 211-244. (Russian)
18. Inductive methods for the Hardy inequality on trees. Ufim. Math. J. (in print)
Preprints:
1. Contraction operator and boundary values. Preprint, Sobolev Inst. of Math. Russian Acad. Sci., Siberian Branch, Novosibirsk, 2005, no. 155, 54 p. (Russian)
2. The Dirichlet problem in bad domains with Muckenhoupt-type weights. Preprint, Sobolev Inst. of Math. Russian Acad. Sci., Siberian Branch, Novosibirsk, 2011, no. 274, 71 p. (Russian)