1. Garain, Prashanta; Some qualitative and quantitative properties of weak solutions to mixed anisotropic and nonlocal quasilinear elliptic and doubly nonlinear parabolic equations, (accepted in Nonlinear Analysis).
2. Biswas, Sanjit ; Garain, Prashanta; Regularity and existence for semilinear mixed local-nonlocal equations with variable singularities and measure data, (accepted in Communications in Contemporary Mathematics).
3. Garain, Prashanta; Lindgren, Erik; Tavakoli, Alireza; Higher Hölder regularity for a subquadratic nonlocal parabolic equation, J. Differ. Equations 419, 253-290 (2025).
4. 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.
5. 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.
6. 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. 
7. 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).
8. 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.
9. 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.
10. Garain, Prashanta; Kinnunen, Juha; Weak Harnack inequality for a mixed local and nonlocal parabolic equation, J. Differential Equations 360 (2023), 373-406.
11. 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. 
12. 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.
13. Bal, Kaushik; Garain, Prashanta; Weighted anisotropic Sobolev inequality with extremal and associated singular problems, Differential Integral Equations 36 (2023), no.1-2, 59–92. 
14. 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.
15. 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. 
16. 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. 
17. 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.
18. 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. 
    

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

• Analysis of elliptic and parabolic partial differential equations.

• Postdoc: Dr. Gurdev Chand Anthal.
• MS thesis student: Sreeram Jaikisan (IISER Berhampur).

• 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.

• Assistant Professor: IIT Indore, India.

• 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.