Profile picture for user rakesh.mat

Dr. Rakesh Arora

Assistant Professor
Department of Mathematical Sciences, IIT(BHU)
Phone No(s): 9971147742
Email: rakesh.mat@iitbhu.ac.in
Area of Interest: Analysis of Partial differential equations, Functional Analysis
                    Vist my Website

Present position:

  • Assistant Professor, Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi: August 2022 - Present.

Past position:

  • Postdoctoral Fellow: Masaryk University, Czech Republic. (Dec. 2020-July-2022), Mentor: Prof. Phouc-Tai Nguyen

Education: 

  • Ph.D. : UPPA, France (2017-20) (Thesis supervisor: Prof. Jacques Giacomoni and Prof. Guillaume Warnault)

  • M.Sc. : IIT Delhi (2015-17).

  • B.Sc. : University of Delhi (2012-15). 

Publications:

  • R. Arora, P.T. Nam, and P.T. Nguyen, Semiclassical Moser-Trudinger inequalities, Transactions of American Mathematical Society, Volume 377, Number 5, May 2024, Pages 3243–3260.

  • R. Arora and S. Shmarev, Double-phase parabolic equations with variable growth and non-linear sources, Adv. Nonlinear Anal., 2023 (12), 304–335. 

  • R. Arora and S. Shmarev, Existence and regularity results for a class of parabolic problems with double phase flux of variable growth, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. (2023) 117:34.

  • R. Arora and S. Shmarev, Existence and global second-order regularity for anisotropic parabolic equations with variable growth, Journal of differential equations 349 (2023), 83-124.

  • R. Arora, A. Fiscella, T. Mukherjee, P. Winkert, Existence of ground state solutions for a Choquard double phase problem, Nonlinear Anal. Real World Appl. 73 (2023), 103914, 22 pp.

  • R. Arora, A. Fiscella, T. Mukherjee, P. Winkert, On double phase Kirchhoff problems with singular nonlinearity, Adv. Nonlinear Anal., vol. 12, no. 1, 2023, pp. 20220312.

  • R. Arora and V.D. Radulescu, Combined effects in mixed local-nonlocal stationary problems, Proceeding of Royal Society of Edinburgh Section A, (2023), 1-47.

  • R. Arora, Multiplicity results for nonhomogeneous elliptic equations with singular nonlinearities, Commun. Pure Appl. Anal., Vol. 21, No. 6, June 2022, pp. 2253–2269. 

  • R. Arora, A. Fiscella, T. Mukherjee, P. Winkert, On critical double phase Kirchhoff problems with singular nonlinearity, Rend. Circ. Mat. Palermo, Series 2, (2022).

  • R. Arora and P. T. Nguyen, Existence and multiplicity results for nonlocal Lane-Emden Systems, Acta Math Vietnam (2022).

  • R. Arora and S. Shmarev, Strong solutions of evolution equations with p(x,t)-Laplacian: existence, global higher integrability of the gradients and second-order regularity, J. Math. Anal. Appl., 493 (2021), 124506.

  • R. Arora, J. Giacomoni and G. Warnault, Regularity results for a class of nonlinear fractional Laplacian and singular problems, Nonlinear Differ. Equ. Appl. 28, 30 (2021).

  • R. Arora, J. Giacomoni, G. Warnault,  A Picone identity for variable exponent operators and applications, Adv. Nonlinear Anal. 9 (2020), 327-360.

  • R. Arora, J. Giacomoni, G. Warnault, Doubly nonlinear equation involving $p(x)$- homogeneous operators: local existence, uniqueness and global behavior, J. Math. Anal. Appl., 487 (2020), 124009.

  • R. Arora, J. Giacomoni, T. Mukherjee, K. Sreenadh, Polyharmonic Kirchhoff type Choquard equations involving exponential nonlinearity with singular weights, Nonlinear Analysis, 196 (2020), 111779.

  • R. Arora, J. Giacomoni,  T. Mukherjee K. Sreenadh, Adams-Moser-Trudinger inequality in the Cartesian product of Sobolev space and its applications}, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. (2020) 114:111.

  • R. Arora, J. Giacomoni, D.Goel and K. Sreenadh, Symmetry of solutions to singular fractional elliptic equations and applications, Comptes Rendus Mathematique, Volume 358, issue 2 (2020), p. 237-243.

  • R. Arora, J. Giacomoni, D. Goel and K. Sreenadh, Positive solutions of 1-D Half-Laplacian equation with singular exponential nonlinearity, Asymptot. Anal., 1 (2019) 1-34.

  • R. Arora, J. Giacomoni, T. Mukherjee and K. Sreenadh, n-Kirchhoff-Choquard equations with exponential nonlinearity, Nonlinear Analysis, 186 (2019), 113-144.

Preprints/ Accepted:

  • R. Arora. P.T. Nguyen and V.D. Radulescu, A large class of nonlocal elliptic equations with singular nonlinearities, https://arxiv.org/pdf/2211.06634.pdf (2022).

  • R. Arora and S. Shmarev, Optimal global second-order regularity and improved integrability for parabolic equations with variable growth, https://arxiv.org/pdf/2305.10877.pdf (2023).

  • R. Arora, A. Crespo-Blanco and P. Winkert, On Logarithmic double phase problems, submitted (2023).

Courses Taught at IIT Varanasi (2022- present):

  • MA101: Engineering Mathematics-I (Fall - 2022, Spring - 2023, Fall-2023)

  • MA203: Mathematical Methods (Spring - 2023)

  • MA 201: Numerical techniques (Fall - 2023, Spring 2023).

Courses Taught at Masarykova Univerzita, Brno, Czech Republic (2021-2022):

  • M8300: Partial differential equations (Winter - 2021)

  • M8300: Partial differential equations (Winter - 2022)

Exploratory project:

  1. Anish Dixit (2022-23): Ordinary differential equations and their applications in Neural Networks.
  2. Aayushi Mahajan (2022-23): Ordinary differential equations and their applications in Neural Networks.
  3. Sanyam Jain (2023-24): Sofa Moving Problem.
  4. Rishi Sahu (2023-24): Goat Grazing Problem.
  5. Jatin Gupta (2023-24): A brief analysis of ODE's.

UG/Stream project:

  1. Adarsh Gupta (2022-23): Partial differential equations and specular derivatives.
  2. Aditya Gautam (2022-23): Partial differential equations and specular derivatives.
  3. Daksh Chaudhary (2023-24): 
  4. Sanskriti Mahajan (2023-24)

M.Tech. thesis: 

  1. Sunny Kumar (2022-): Machine learning and its applications.
  2. Adarsh Gupta (2023-)
  3. Aditya Gautam (2023-)

Ph.D.:

  1. Nitin Kumar Maurya (2022-)
  2. Arshi Vaishnavi (2022-)