### Research Interest

Dr. Durvudkhan Suragan received his Ph.D. in mathematics from Al-Farabi Kazakh National University in 2013. He has a master degree (with distinction) in theoretical physics from King’s College London. Prior to joining Nazarbayev University in April 2018, he served in the Department of Mathematics at Imperial College London as a research associate and at Institute of Mathematics and Mathematical Modeling (Almaty) as a leading researcher. His current research interests include analysis on Lie groups, applied mathematics (mathematical physics), PDE, potential theory and spectral geometry.

In 2013, Suragan was awarded the Konayev prize for young scientists (in Kazakhstan) for the best work in the field of natural sciences.

In 2018, Suragan won the Ferran Sunyer i Balaguer Prize. The prize is awarded for a mathematical monograph of an expository nature presenting the latest developments in an active area of research in Mathematics, in which the applicant has made important contributions. Suragan won the prize for his (with Professor Michael Ruzhansky, Imperial College London) monograph: Hardy inequalities on homogeneous groups, Progress in Mathematics, Vol. 327, Birkhauser, 2019. xvi+588pp.

Isoperimetric Inequalities for Some Integral Operators Arising in Potential Theory

Michael Ruzhansky, Durvudkhan Suragan, **2017** In : Functional Analysis in Interdisciplinary Applications216, p. 320-329

On S-Number Inequalities of Triangular Cylinders for the Heat Operator

Tynysbek Kal’menov, Aidyn Kassymov, Durvudkhan Suragan, **2017** In : Functional Analysis in Interdisciplinary Applications216, p. 349-362

A boundary condition and spectral problems for the Newton potential

T. Sh Kalmenov, D. Suragan, **2011** In : Modern Aspects of the Theory of Partial Differential Equations, p. 187-210

Euler semigroup, Hardy–Sobolev and Gagliardo–Nirenberg type inequalities on homogeneous groups

Michael Ruzhansky, Durvudkhan Suragan, Nurgissa Yessirkegenov, **2020** In : . 101 , p.1 , p. 162-191

Fractional logarithmic inequalities and blow-up results with logarithmic nonlinearity on homogeneous groups

Aidyn Kassymov, Michael Ruzhansky, Durvudkhan Suragan, **2020** In : . 27 , p.1

Hardy and Rellich inequalities for anisotropic p-sub-Laplacians

M. Ruzhansky, B. Sabitbek, D. Suragan, **2020** In : . 14 , p.2 , p. 380-398

Lyapunov-type inequalities for the fractional p-sub-Laplacian

Aidyn Kassymov, Durvudkhan Suragan, **2020** In : . 5 , p.2 , p. 435-452

Multidimensional inverse Cauchy problems for evolution equations

Mukhtar Karazym, Tohru Ozawa, Durvudkhan Suragan, **2020** In : . 28 , p.11 , p. 1582-1590

Oscillatory solutions of fractional integro-differential equations

Joel E. Restrepo, Durvudkhan Suragan, **2020** In : . 43 , p.15 , p. 9080-9089

Subelliptic geometric Hardy type inequalities on half-spaces and convex domains

Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan, **2020** In : . 11 , p.4 , p. 1042-1061

Trace formulae of potentials for degenerate parabolic equations

Mukhtar Karazym, Durvudkhan Suragan, **2020** In : . 33 , p.7-8 , p. 337-360

Green’s Identities, Comparison Principle and Uniqueness of Positive Solutions for Nonlinear p-sub-Laplacian Equations on Stratified Lie Groups

Michael Ruzhansky, Durvudkhan Suragan, **2019** In : . 53 , p.2 , p. 645-658

Hardy–Littlewood–Sobolev and Stein–Weiss inequalities on homogeneous Lie groups

Aidyn Kassymov, Michael Ruzhansky, Durvudkhan Suragan, **2019** In : . 30 , p.8 , p. 643-655

L
^{p}
-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups

Tohru Ozawa, Michael Ruzhansky, Durvudkhan Suragan, **2019** In : . 70 , p.1 , p. 305-318

On spectral and boundary properties of the volume potential for the Helmholtz equation

Tynysbek Sharipovich Kalmenov, Michael Ruzhansky, Durvudkhan Suragan, **2019** In : . 14 , p.5

Weighted anisotropic Hardy and Rellich type inequalities for general vector fields

Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan, **2019** In : . 26 , p.2

Weighted L^{p} -Hardy and L^{p} -Rellich inequalities with boundary terms on stratified Lie groups

Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan, **2019** In : . 32 , p.1 , p. 19-35

A comparison principle for nonlinear heat Rockland operators on graded groups

Michael Ruzhansky, Durvudkhan Suragan, **2018** In : . 50 , p.5 , p. 753-758

A note on stability of Hardy inequalities

Michael Ruzhansky, Durvudkhan Suragan, **2018** In : .

Elements of Potential Theory on Carnot Groups

M. V. Ruzhansky, D. Suragan, **2018** In : . 52 , p.2 , p. 158-161

Extended Caffarelli-Kohn-Nirenberg inequalities, and remainders, stability and superweights for Lp-weighted Hardy inequalities

Durvudkhan Suragan, Michael Ruzhansky, Nurgissa Yessirkegenov, **2018** In : . 5 , p. 32-62

Green-type identities for Rockland operators on graded Lie groups

Manat Mustafa, Durvudkhan Suragan, **2018** In : . , p. 1-8

Hardy-Littlewood, Bessel-Riesz, and fractional integral operators in anisotropic Morrey and Campanato spaces

Durvudkhan Suragan, Michael Ruzhansky, Nurgissa Yessirkegenov, **2018** In : . , p. 577-612

Horizontal Weighted Hardy–Rellich Type Inequalities on Stratified Lie Groups

Bolys Sabitbek, Durvudkhan Suragan, **2018** In : . 12 , p.6 , p. 1469-1480

Isoperimetric inequalities for the cauchy-dirichlet heat operator

Tynysbek Sh Kal’menov, Aidyn Kassymov, Durvudkhan Suragan, **2018** In : . 32 , p.3 , p. 885-892

Isoperimetric inequalities for the heat potential operator

Tynysbek Sh Kal’menov, Aidyn Kassymov, Durvudkhan Suragan, **2018** In : . 32 , p.3 , p. 903-910

$L^{p}$-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups

Tohru Ozawa, Michael Ruzhansky, Durvudkhan Suragan, **2018** In : .

Sobolev Type Inequalities, Euler–Hilbert–Sobolev and Sobolev–Lorentz–Zygmund Spaces on Homogeneous Groups

Michael Ruzhansky, Durvudkhan Suragan, Nurgissa Yessirkegenov, **2018** In : . 90 , p.1

Anisotropic L ^{2} -weighted Hardy and L ^{2} -Caffarelli-Kohn-Nirenberg inequalities

Michael Ruzhansky, Durvudkhan Suragan, **2017** In : . 19 , p.6

Caffarelli–Kohn–Nirenberg and Sobolev type inequalities on stratified Lie groups

Michael Ruzhansky, Durvudkhan Suragan, Nurgissa Yessirkegenov, **2017** In : . 24 , p.5

Geometric maximizers of Schatten norms of some convolution type integral operators

Michael Ruzhansky, Durvudkhan Suragan, **2017** In : . 456 , p.1 , p. 444-456

Hardy and Rellich inequalities, identities, and sharp remainders on homogeneous groups

Michael Ruzhansky, Durvudkhan Suragan, **2017** In : . 317 , p. 799-822

Inégalités de Caffarelli–Kohn–Nirenberg étendues et super-poids des inégalités de Hardy L^{p}-pondérées

Michael Ruzhansky, Durvudkhan Suragan, Nurgissa Yessirkegenov, **2017** In : . 355 , p.6 , p. 694-698

Inequalities for the eigenvalues of the Riesz potential

T. Sh Kal’menov, D. Suragan, **2017** In : . 102 , p.5-6 , p. 770-775

Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups

Michael Ruzhansky, Durvudkhan Suragan, **2017** In : . 308 , p. 483-528

Local hardy and rellich inequalities for sums of squares of vector fields

Michael Ruzhansky, Durvudkhan Suragan, **2017** In : . 22 , p.7-8 , p. 505-540

On Green functions for Dirichlet sub-Laplacians on H-type groups

Nicola Garofalo, Michael Ruzhansky, Durvudkhan Suragan, **2017** In : . 452 , p.2 , p. 896-905

On horizontal Hardy, Rellich, Caffarelli–Kohn–Nirenberg and p-sub-Laplacian inequalities on stratified groups

Michael Ruzhansky, Durvudkhan Suragan, **2017** In : . 262 , p.3 , p. 1799-1821

On Isoperimetric Inequalities for the Cauchy-Robin Heat Operator

A. Kassymov, M. Sadybekov, D. Suragan, **2017** In : . 12 , p.3 , p. 114-118

Some Spectral Geometry Inequalities for Generalized Heat Potential Operators

Aidyn Kassymov, Durvudkhan Suragan, **2017** In : . 11 , p.6 , p. 1371-1385

Uncertainty relations on nilpotent Lie groups

Michael Ruzhansky, Durvudkhan Suragan, **2017** In : . 473 , p.2201

Communications of the Moscow mathematical society

M. V. Ruzhansky, D. Suragan, **2016** In : . 71 , p.1 , p. 157-158

Isoperimetric inequalities for Schatten norms of Riesz potentials

G. Rozenblum, M. Ruzhansky, D. Suragan, **2016** In : . 271 , p.1 , p. 224-239

Isoperimetric inequalities for the logarithmic potential operator

Michael Ruzhansky, Durvudkhan Suragan, **2016** In : . 434 , p.2 , p. 1676-1689

On first and second eigenvalues of Riesz transforms in spherical and hyperbolic geometries

Michael Ruzhansky, Durvudkhan Suragan, **2016** In : . 6 , p.2 , p. 325-334

On KAC’S principle of not feeling the boundary for the kohn laplacian on the heisenberg group

Michael Ruzhansky, Durvudkhan Suragan, **2016** In : . 144 , p.2 , p. 709-721

On permeable potential boundary conditions for the Laplace–Beltrami operator

T. Sh Kal’menov, D. Suragan, **2015** In : . 56 , p.6 , p. 1060-1064

On spectral geometry for the one-speed particle transport operator

D. Suragan, **2015** In : . 55 , p.5 , p. 844-847

Initial-boundary value problems for the wave equation

Tynysbek Sh Kalmenov, Durvudkhan Suragan, **2014** In : . 2014

On eigenvalue problems of the one-speed neutron transport equation for isotropic scattering

D. Suragan, **2013** In : . 62 , p. 468-470

On transparent boundary conditions for the high-order heat equation

D. Suragan, N. Tokmagambetov, **2013** In : . 10 , p.1 , p. 141-149

Boundary conditions for the volume potential for the polyharmonic equation

T. Sh Kal'menov, D. Suragan, **2012** In : . 48 , p.4 , p. 604-608

On a new method for constructing the Green function of the Dirichlet problem for the polyharmonic equation

T. Sh Kal'menov, D. Suragan, **2012** In : . 48 , p.3 , p. 441-445

To spectral problems for the volume potential

T. Sh Kal'menov, D. Suragan, **2009** In : . 80 , p.2 , p. 646-649

Determination of the structure of the spectrum of regular boundary value problems for differential equations by V.A. Il'in's method of anti-a priori estimates

T. Sh Kal'menov, D. Suragan, **2008** In : . 78 , p.3 , p. 913-915

- Oscillatory solutions of generalized fractional integro-differential equations,
*Mathematical Methods in the Applied Sciences*, DOI: 10.1002/mma.6602 (2020). (with Restrepo J.) - Multidimensional inverse Cauchy problems for evolution equations,
*Inverse Problems in Science and Engineering*, DOI: 10.1080/17415977.2020.1739034 (2020). (with Karazym M. and Ozawa T.) - Extended Caffarelli-Kohn-Nirenberg inequalities, and remainders, stability and superweights for Lp-weighted Hardy inequalities,
*Transactions of the American Mathematical Society*, Ser. B, 5 (2018), 32-62. (with Ruzhansky M. and Yessirkegenov N.) - Layer potentials, Green formulae, Kac problem, and refined Hardy inequality on homogeneous Carnot groups,
*Advances in Mathematics*, 308 (2017), 483-528. (with Ruzhansky M.) - Uncertainty relations on nilpotent Lie groups,
*Proceedings of the Royal Society A*, 473 (2017), no. 2201, 20170082. (with Ruzhansky M.) - On horizontal Hardy, Rellich, Caffarelli-Kohn-Nirenberg and p-sub-Laplacian inequalities on stratified groups,
*Journal of Differential Equations*, 262 (2017), 1799-1821. (with Ruzhansky M.) - Anisotropic L2-weighted Hardy and L2-Caffarelli–Kohn–Nirenberg inequalities,
*Communications in Contemporary Mathematics*, 19:06 (2017), 1750014. (with Ruzhansky M.) - Isoperimetric inequalities for Schatten norms of Riesz potentials,
*Journal of Functional Analysis*, 271 (2016), 224-239. (Rozenblum G. and Ruzhansky M.) - Transfer of Sommerfeld radiation conditions to the boundary of a bounded domain,
*Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki*, 52:6 (2012), 1063-1068. (with T.Sh. Kal’menov) - Determination of the structure of the spectrum of regular boundary value problems for differential equations by VA Il’in’s method of anti-a priori estimates,
*Doklady Mathematics*78:3 (2008), 913-915. (with T.Sh. Kal’menov)

Calculus I, Linear Algebra with Applications