7 papers
Carleman estimates for sub-Laplacians on Carnot groups
Vedansh Arya, Dharmendra Kumar
In this note, we establish a new Carleman estimate with singular weights for the sub-Laplacian on a Carnot group for functions satisfying the discrepancy assumption in…
Existence of variational solutions to doubly nonlinear nonlocal evolution equations via minimizing movements
Suchandan Ghosh, Dharmendra Kumar, Harsh Prasad +1
We prove existence of variational solutions for a class of doubly nonlinear nonlocal evolution equations whose prototype is the double phase equation \begin{align*} \partial_t u^m…
Borderline gradient continuity for fractional heat type operators
Vedansh Arya, Dharmendra Kumar
In this paper, we establish gradient continuity for solutions to \[ (\partial_t - \operatorname{div}(A(x) \nabla u))^s =f,\ s \in (1/2, 1), \] when belongs to the scaling criti…
Boundary differentiability of solutions to elliptic equations in convex domains in the borderline case
Dharmendra Kumar
In this work, we consider the following elliptic partial differential equations: \begin{equation*} \left\{ \begin{aligned}{} - b_{ij} \; \frac{\partial^{2} w}{\partial x_{i} \parti…
New solitary wave and Multiple soliton solutions of (3 + 1)-dimensional KdV type equation by using Lie symmetry approach
Sachin Kumar, Dharmendra Kumar
Solitary waves are localized gravity waves that preserve their consistency and henceforth their visibility through properties of nonlinear hydrodynamics. Solitary waves have finite…
Lie symmetry analysis and new periodic solitary wave solutions of (3+1)-dimensional generalized shallow water wave equation
Sachin Kumar, Dharmendra Kumar
Many important physical situations such as fluid flows, marine environment, solid-state physics and plasma physics have been represented by shallow water wave equation. In this art…