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).

Education: 

• Ph.D. : UPPA, France (2017-20). (Thesis supervisior: Prof. Jacques Giacomoni and Prof. Guillaume Warnault)
• M.Sc. : IIT Delhi (2015-17).
• B.Sc. : Univeristy of Delhi (2012-15). 

Publications:

(2023)

• R. Arora and S. Shmarev, Double-phase parabolic equations with variable growth and non-linear sources, accepted in Adv. Nonlinear Anal.

(2022)

• 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).   

(2021)

• 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).

(2020)

• 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 Cartesian product of Sobolev space and its applications}, RACSAM. 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 Math\'ematique, Volume 358, issue 2 (2020), p. 237-243.

(2019)

• 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, A. Fiscella, T. Mukherjee, P. Winkert, On double phase Kirchhoff problems with singular nonlinearity, https://arxiv.org/pdf/2111.07565.pdf, (2021).
• R. Arora and S. Shmarev, Existence and regularity results for a class of parabolic problems with double phase flux of variable growth, https://arxiv.org/pdf/2109.03597.pdf (2021).
• R. Arora and V.D. Radulescu, Combined effects in mixed local-nonlocal stationary problems, https://arxiv.org/pdf/2111.06701.pdf, (2021).
• R. Arora and S. Shmarev, Existence and global second-order regularity for anisotropic parabolic equations with variable  growth, https://arxiv.org/pdf/2208.07723.pdf (2022).