2 citations · 4 across the 12 of their papers we have counts for
13 papers
Harnack Inequality for Parabolic Fractional -Laplace Equations
Harsh Prasad
We establish an intrinsic Harnack inequality with an optimal tail term for weak solutions of parabolic fractional -Laplace equations with and whose kernels are…
Strong Unique Continuation for Fractional Schrödinger Operators
Harsh Prasad
We prove the strong unique continuation property for the fractional Schrödinger equation \[ (-Δ)^s u=Vu \] with scaling-critical potentials …
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…
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 \…
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…
Lipschitz potential estimates for diffusion with jumps
Nirjan Biswas, Harsh Prasad
For and , we consider the following mixed local-nonlocal equation where is…
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{…
On The Weak Harnack Estimate For Nonlocal Equations
Harsh Prasad
We prove a weak Harnack estimate for a class of doubly nonlinear nonlocal equations modelled on the nonlocal Trudinger equation \begin{align*} \partial_t(|u|^{p-2}u) + (-Δ_p)^s u =…
Local Hölder regularity for nonlocal parabolic -Laplace equations
Karthik Adimurthi, Harsh Prasad, Vivek Tewary
We prove local Hölder regularity for a nonlocal parabolic equations of the form \begin{align*} \partial_t u + \text{P.V.}\int_{\mathbb{R}^N} \frac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,…
Hölder regularity for fractional -Laplace equations
Karthik Adimurthi, Harsh Prasad, Vivek Tewary
We give an alternative proof for Hölder regularity for weak solutions of nonlocal elliptic quasilinear equations modelled on the fractional p-Laplacian where we replace the discret…
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…
Local boundedness of variational solutions to nonlocal double phase parabolic equations
Harsh Prasad, Vivek Tewary
We prove local boundedness of variational solutions to the double phase equation \begin{align*} \partial_t u +& P.V.\int_{\mathbb{R}^N}\frac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|…