6 papers
Global UCP For Parabolic Fractional -Laplace Equation With Very Rough Potentials
Harsh Prasad
We show that the global unique continuation principle holds for the parabolic fractional Laplace equation with very rough potentials . Whereas t…
Lipschitz potential estimates for diffusion with jumps
Nirjan Biswas, Harsh Prasad
For and , we consider the following mixed local-nonlocal equation where $Ω\subset \mathbb{R}^d…
Logarithmic continuity for the Nonlocal degenerate two-phase Stefan problem
Kyeongbae Kim, Ho-Sik Lee, Harsh Prasad
We establish certain oscillation estimates for weak solutions to nonlinear, anomalous phase transitions modeled on the nonlocal two-phase Stefan problem. The problem is singular in…
Local Hölder Regularity For Nonlocal Porous Media And Fast Diffusion Equations With General Kernel
Kyeongbae Kim, Ho-Sik Lee, Harsh Prasad
We show that locally bounded, local weak solutions to certain nonlocal, nonlinear diffusion equations modeled on the fractional porous media and fast diffusion equations given by \…
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…