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Dr. Prasanta Garain

Assistant Professor

Mathematical Sciences

prashanta@iiserbpr.ac.in

Personal Website

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Academic Background

  • Postdoctoral research experiences: Uppsala University, Sweden. Ben Gurion University of the Negev, Israel, Aalto University, Finland, TIFR CAM Bangalore, India.

  • Ph.D in Mathematics, IIT Kanpur, India.

  • M.Sc in Mathematics, IIT Kanpur, India.

  • B.Sc in Mathematics Hons, Jagannath Kishore College, University of Burdwan, India.

Professional Experience 

  • Assistant Professor: IIT Indore, India.

Awards and Memberships

  • NBHM Ph.D. Fellowship in 2014.

  • Qualified CSIR-JRF in 2014.

  • Qualified GATE in 2014.

  • Awarded Bishnupada Ray Memorial Trust Fund Prize for the year 2012 for securing highest marks among all UG Hons. Students of Jagannath Kishore College, University of Burdwan, India.

  • Awarded Manindralal Banerjee Memorial Prize for the year 2012 for securing highest marks among all UG Hons. Students of any college of Purulia District, India.

Research Interests

  • Analysis of elliptic and parabolic partial differential equations.

Research Group

  • Postdoc: Dr. Gurdev Chand Anthal.

  • MS thesis student: Sreeram Jaikisan (IISER Berhampur).

About me

Dr. Prashanta Garain is an Assistant Professor in the Department of Mathematical Sciences at the Indian Institute of Science Education and Research Berhampur (IISER Berhampur). Dr. Garain does research in the mathematical analysis of partial differential equations (PDEs). More precisely, he works on the regularity and existence theory for elliptic and parabolic partial differential equations including various type of p-Laplace type equations, nonlinear Kolmogorov-Fokker-Planck type equations, PDEs in metric measure spaces. He has research papers in several international refereed journals, including Transactions of the American Mathematical Society, Proceedings of the American Mathematical Society, Calculus of variations and PDE's, Journal of Differential Equations, Math. Ann., Proceedings of the Edinburgh Mathematical Society, Nonlinear Analysis, Math. Z., Math. Nachr., Journal of Geometric Analysis etc.. Some of them are listed below.

Biography

Dr. Prashanta Garain is an Assistant Professor in the Department of Mathematical Sciences at the Indian Institute of Science Education and Research Berhampur (IISER Berhampur). Prior to this, he was an Assistant Professor in the Department of Mathematics at the Indian Institute of Technology, Indore (IIT Indore).

He did his B.Sc. in Mathematics from Jagannath Kishore College, Purulia under the University of Burdwan. He has completed his M.Sc. in Mathematics and Ph.D. in Mathematics from the Indian Institute of Technology, Kanpur. Dr. Garain has postdoctoral research experiences from TIFR CAM, Bangalore, India, Aalto University, Finland, Ben Gurion University of the Negev, Israel and Uppsala University, Sweden.

Research Projects

Mixed local and nonlocal problems, Seed Grant from IISER Berhampur.

Key Publications


Garain Prashanta; Pchelintsev Valerii, Ukhlov Alexander, On the Neumann (p,q) -eigenvalue problem in Hölder singular domains, Calc. Var. Partial Differential Equations 63  (2024), no. 7, Paper No. 172, 17 pp.

Garain Prashanta, Lindgren Erik; Higher Hölder regularity for the fractional p-Laplace equation in the subquadratic case,  Math. Ann. 390 (2024), no. 4, 5753–5792.

Garain, Prashanta; Kinnunen, Juha; On the regularity theory for mixed local and nonlocal quasilinear parabolic equations, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 25 (2024), no. 1, 495–540. 

Garain, Prashanta, Kim, Wontae, Kinnunen, Juha; On the regularity theory for mixed anisotropic and nonlocal p-Laplace equations and its applications to singular problems, Forum Math. 36, No. 3, 697-715 (2024).

Garain, Prashanta; On a class of mixed local and nonlocal semilinear elliptic equation with singular nonlinearity, J. Geom. Anal. 33 (2023), no. 7, Paper No. 212, 20 pp.

Garain, Prashanta; Lindgren, Erik; Higher Holder regularity for mixed local and nonlocal degenerate elliptic equations, Calc. Var. Partial Differential Equations 62 (2023), no. 2, Paper No. 67, 36 pp.

Garain, Prashanta; Kinnunen, Juha; Weak Harnack inequality for a mixed local and nonlocal parabolic equation, J. Differential Equations 360 (2023), 373-406.

Garain, Prashanta;  Nyström, Kaj; On regularity and existence of weak solutions to nonlinear Kolmogorov-Fokker-Planck type equations with rough coefficients, Math. Eng. 5 (2023), no.2, Paper No. 043, 37 pp. 

Banerjee, Agnid, Garain, Prashanta, Kinnunen, Juha, Lower semicontinuity and pointwise behavior of supersolutions for some doubly nonlinear nonlocal parabolic p-Laplace equations, Commun. Contemp. Math. 25 (2023), no. 8,  Paper No. 2250032, 23 pp.

Bal, Kaushik; Garain, Prashanta; Weighted anisotropic Sobolev inequality with extremal and associated singular problems, Differential Integral Equations 36 (2023), no.1-2, 59–92. 

Garain, Prashanta; Kinnunen, Juha; On the regularity theory for mixed local and nonlocal quasilinear elliptic equations, Trans. Amer. Math. Soc. 375 (2022), no. 8, 5393–5423.

Garain, Prashanta; Ukhlov, Alexander; Mixed local and nonlocal Sobolev inequalities with extremal and associated quasilinear singular elliptic problems, Nonlinear Anal.223 (2022), Paper No. 113022, 35 pp. 

Banerjee, Agnid; Garain, Prashanta; Kinnunen, Juha; Some local properties of subsolutons and supersolutions for a doubly nonlinear nonlocal parabolic p-Laplace equation, Ann. Mat. Pura Appl. (4) 201 (2022), no.4, 1717–1751. 

Alves, Claudianor O.; Garain, Prashanta and Vicentiu D. Radulescu; High perturbations of quasilinear problems with double criticality, Math. Z. 299 (2021), no. 3-4, 1875–1895.

Garain, Prashanta; Kinnunen, Juha; Nonexistence of variational minimizers related to a quasilinear singular problem in metric measure spaces, Proc. Amer. Math. Soc.149 (2021), no.8, 3407–3416.

Contact Details

Full Name

Prasanta Garain


Email

prashanta@iiserbpr.ac.in


Address

IISER Berhampur


Personal Website

https://sites.google.com/view/pgarain/home