4 papers
Mixed Local-Nonlocal Parabolic Equations in Heisenberg Group : Harnack Inequality with an Optimal Tail
Debraj Kar
We prove Harnack inequality with an optimal tail for linear mixed local-nonlocal parabolic equation on the Heisenberg group. For this purpose, we make use of the expansion of posit…
Optimal in tail Hölder estimates for weak solutions of the nonlocal parabolic p-Laplace equations on the Heisenberg group
Debraj Kar
We prove the Hölder continuity for weak solutions to parabolic p-Laplace equations on the Heisenberg group. We deduce this result while considering an optimal tail condition.
Nonlocal Quasilinear Parabolic Equations in Heisenberg Group: Local Boundedness with an Optimal Tail
Debraj Kar, Vivek Tewary
We prove local boundedness for a quasilinear parabolic equation on the Heisenberg group \[ \partial_t u(ξ,t) + \text{p.v.}\int_{\mathbb{H}^N} \frac{|u(ξ,t)-u(η,t)|^{p-2}(u(ξ,t)-u(η…
Regularity results to the class of variational obstacle problems with variable exponent
Debraj Kar
In this paper we prove local gradient estimates and higher differentiability result for the solutions of variational obstacle inequalities \int_Ω\big<\mathcal{A}(x,u,Du),D(ϕ-u)\big…