Publications and preprints

Published/ accepted  papers

(with M. Modasiya)  Fine boundary regularity for fully nonlinear mixed local-nonlocal problems, to appear in Journal of Differential Equations.  https://arxiv.org/abs/2301.02397

(with B. Kim and  J. Oh) Parabolic Lipschitz truncation for multi-phase problems: the degenerate case, to appear in  Advances in Calculus of Variations. https://doi.org/10.1515/acv-2025-0003

Gradient higher integrability for degenerate/ singular parabolic multi-phase problems, appeared in Journal of Geometric Analysis. 35, 170 (2025).  https://doi.org/10.1007/s12220-025-01950-4

(with A. Sen)  Existence of global entropy solution for Eulerian droplet models and two-phase flow model with non-constant air velocity, appeared in  Journal of  Dynamics and Differential Equations. https://doi.org/10.1007/s10884-023-10337-4

(with M. R. Sahoo and M. Singh) Initial boundary value problem for 1D scalar balance laws with strictly convex flux, appeared in Journal of  Mathematical Analysis and Applications. https://doi.org/10.1016/j.jmaa.2023.128006

A note on Hopf's lemma and strong minimum principle for nonlocal equations with non-standard growth, appeared in Forum Mathematicum. https://doi.org/10.1515/forum-2022-0331

(with A. Biswas and M. Modasiya) Boundary regularity of mixed local-nonlocal operators and its application, Annali di Matematica Pura ed Applicata.  202, 679–710.  https://doi.org/10.1007/s10231-022-01256-0

(with L. Neumann,  M. Oberguggenberger and M. R. Sahoo) Initial-boundary value problem for 1D pressureless gas dynamics, Journal of  Differential Equations. 316, 687–725. https://doi.org/10.1016/j.jde.2022.01.058

(with A. Aggarwal M. R.  Sahoo and G. Vaidya) Solutions with concentration for conservation laws with discontinuous flux and its applications to numerical schemes for hyperbolic systems. Studies in  Applied Mathematics. 145, no. 2, 247–290. https://doi.org/10.1111/sapm.12319

(with M. R. Sahoo) Vanishing viscosity limit for a system of balance laws with general type initial data arising from 1D Saint-Venant model. Journal of Mathematical  Physics. 61 (2020), no. 5, 051507, 19 pp. https://doi.org/10.1063/1.5141052

(with M. R. Sahoo)  Limiting behavior of scaled general Euler equations of compressible fluid flow.  Z. Angew. Math. Phys. 71, no. 2, Paper No. 51, 19 pp. https://doi.org/10.1007/s00033-020-1273-1

(with M. R. Sahoo) Limiting behavior of some strictly hyperbolic systems of conservation laws. Asymptotic Analysis. 113, no. 4, 211–238. https://doi.org/10.3233/ASY-181513

(with S. Engu and M. R. Sahoo) On a complex sequence of vanishing moments. Journal of Ramanujan Math. Soc. 34, no. 2, 185–190.

Preprints

1D pressureless gas dynamics systems in a strip, preprint 2025.  https://doi.org/10.48550/arXiv.2502.15927

(with J. Oh) Gradient higher integrability for degenerate parabolic double phase systems with two modulating coefficients, preprint 2025. https://arxiv.org/abs/2504.15799

(with J. Siltakoski) Lipschitz regularity for parabolic double phase equations with gradient nonlinearity, preprint 2025. https://arxiv.org/abs/2508.16391

Manuscripts under preparation

(with S. Jarohs and T. Weth) The logarithmic Laplacian in fractional boundary value problems.

Thesis

Solutions in the class of measures for some hyperbolic systems of conservation laws and scalar conservation laws with discontinuous flux. May 2021,  http://www.hbni.ac.in/phdthesis/math/MATH11201604001.pdf

Notes

Notes on conservation laws. Link