Publications
Research interests
Eigenvalue problems in both local and nonlocal setup.
Nonlocal PDEs.
Functional inequalities like Hardy's, Poincar\'e, Morrey's, and Moser-Trudinger's inequalities in fractional Sobolev spaces.
Fractional Orlicz-Sobolev spaces.
Publications and Preprints
On Morrey's inequality in Sobolev-Slobodeckij spaces, to appear in Journal of Functional Analysis (with L. Brasco and F. Prinari).
On generalized eigenvalue problems of fractional (p,q)-Laplace operator with two parameters, to appear in Proceedings of the Royal Society of Edinburgh Section A: Mathematics (with N. Biswas).
A note on the supersolution method for Hardy's inequality, Revista Matemática Complutense, 37(2024), no. 2, 323 - 340 (with F. Bianchi, L. Brasco, and A. C. Zagati).
A system of equations involving the fractional p-Laplacian and doubly critical nonlinearities, Advanced Nonlinear Studies, 23(2023), no. 1, paper no. 20230103, 24 pp (with M. Bhakta and K. Perera).
Characterization of fractional Sobolev-Poincar\'e and (localized) Hardy inequalities, Journal of Geometric Analysis, 33(2023), no. 7, paper no. 223.
Remarks on the fractional Moser-Trudinger inequality, Journal d'Analyse Mathematique, 148(2022), no. 2, 447-470.
Hardy and Poincar\'e inequalities in fractional Orlicz-Sobolev space, Nonlinear Analysis, 216(2022), paper no. 112697, 22 pp (with K. Bal, K. Mohanta, and P. Roy)
On the best constant in fractional p- Poincar\'e inequalities on cylindrical domains, Differential and Integral Equations, 34(2021), no. 11/12, 691-712 (with K. Mohanta).
On the asymptotic behavior of the eigenvalues of nonlinear elliptic problems in domains becoming unbounded, Asymptotic Analysis, 123(2021), no. 1-2, 79-94 (with L. Esposito and P. Roy).
Study of fractional Poincar\'e inequalities on unbounded domains, Discrete and Continuous Dynamical Systems. Series A, 41(2021), no. 6, 2993-3020 (with I. Chowdhury, G. Csat\'o and P. Roy).