4 papers · 1 filter
Equivalence of weak and viscosity solutions for nonlocal p-Laplace type equations on the Heisenberg group
Debangana Mukherjee, Vivek Tewary
We establish the equivalence between weak and viscosity solutions for a broad class of nonlocal -Laplace type equations on the Heisenberg group whose kernels satisfy standard sy…
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)…
Gradient regularity for mixed local-nonlocal quasilinear parabolic equations
Karthik Adimurthi, Harsh Prasad, Vivek Tewary
In this paper, we prove local Hölder continuity for the spatial gradient of weak solutions to $$u_t - \text{div} (|\nabla u|^{p-2}\nabla u) + \text{P.V.} \int_{\mathbb{R}^n} \frac…
A variational approach to nonlocal image restoration flows
Harsh Prasad, Vivek Tewary
We prove existence, uniqueness and initial time regularity for variational solutions to nonlocal total variation flows associated with image denoising and deblurring. In particular…