Garain, Prashanta and Lindgren, Erik; Higher H\"older regularity for fractional (p,q)-Laplace equations, (accepted in Advances in Calculus of Variations, https://doi.org/10.1515/acv-2025-0119).
Garain, Prashanta; Two alternative proofs of weak Harnack inequality for mixed local and nonlocal p-Laplace equations with a nonhomogeneity, J. Differential Equations 477 (2026), Paper No. 114529.
Garain, Prashanta; Some qualitative and quantitative properties of weak solutions to mixed anisotropic and nonlocal quasilinear elliptic and doubly nonlinear parabolic equations, Nonlinear Anal. 256 (2025), Paper No. 113796, 31 pp.Biswas, Sanjit ; Garain, Prashanta; Regularity and existence for semilinear mixed local-nonlocal equations with variable singularities and measure data, Commun. Contemp. Math. 28 (2026), no. 1, Paper No. 2550028, 39 pp. Anthal Chand, Gurdev; Garain, Prashanta; Symmetry, existence and regularity results for a class of mixed local-nonlocal semilinear singular elliptic problem via variational characterization, Math. Z. 311 (2025), no. 1, Paper No. 20, 35 pp.
Garain, Prashanta; Lindgren, Erik; Tavakoli, Alireza; Higher Hölder regularity for a subquadratic nonlocal parabolic equation, J. Differ. Equations 419, 253-290 (2025).
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.
