2 citations · 6 across the 18 of their papers we have counts for
18 papers
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)-u(η…
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…
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 $$u_t - \text{div} (|\nabla u|^{p-2}\nabla u) + \text{P.V.} \int_{\mathbb{R}^n} \frac{…
regularity for quasilinear parabolic equations with nonstandard growth
Karthik Adimurthi, Suchandan Ghosh, Vivek Tewary
In this paper, we obtain estimates for weak solutions of certain quasilinear parabolic equations satisfying nonstandard growth conditions, the prototype examples being $$…
Pointwise and Weighted Hessian Estimates for Kolmogorov-Fokker-Planck type operators
Abhishek Ghosh, Vivek Tewary
In this article, we obtain hessian estimates for Kolmogorov-Fokker-Planck operators in non-divergence form in several Banach function spaces. Our approach relies on a representatio…
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,…
Borderline Lipschitz regularity for bounded minimizers of functionals with (p,q)-growth
Karthik Adimurthi, Vivek Tewary
We prove local Lipschitz regularity for bounded minimizers of functionals with nonstandard -growth with the source term in the Lorentz space under the restriction $q<…
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 nonlocal evolution equations via convex minimization
Harsh Prasad, Vivek Tewary
We prove existence of variational solutions for a class of nonlocal evolution equations whose prototype is the double phase equation \begin{align*} \partial_t u &+ \text{P.V.}\int_…
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))}{|…
On Lipschitz regularity for bounded minimizers of functionals with (p,q) growth
Karthik Adimurthi, Vivek Tewary
We obtain Lipschitz estimates for bounded minimizers of functionals with nonstandard -growth satisfying the dimension-independent restriction with . This r…
Combined Effects of Homogenization and Singular Perturbations : A Bloch Wave Approach
Vivek Tewary
We study Bloch wave homogenization of periodically heterogeneous media with fourth order singular perturbations. We recover different homogenization regimes depending on the relati…
An optimal boundedness result for weak solutions of double phase quasilinear parabolic equations
Karthik Adimurthi, Vivek Tewary
We obtain local boundedness of weak solutions of double phase quasilinear parabolic equations of the form \[u_t-\text{div} \left(|\nabla u|^{p-2}\nabla u+a(x,t)|\nabla u|^{q-2}\nab…
Bloch Wave Homogenization of Quasiperiodic Media
Sivaji Ganesh Sista, Vivek Tewary
Quasiperiodic media is a class of almost periodic media which is generated from periodic media through a "cut and project" procedure. Bloch waves are typically defined through a di…
Bloch wave approach to almost periodic homogenization and approximations of effective coefficients
Sivaji Ganesh Sista, Vivek Tewary
Bloch wave homogenization is a spectral method for obtaining effective coefficients for periodically heterogeneous media. This method hinges on the direct integral decomposition of…
Generic Simplicity of Spectral Edges and Applications to Homogenization
Sivaji Ganesh Sista, Vivek Tewary
We consider the spectrum of a second-order elliptic operator in divergence form with periodic coefficients, which is known to be completely described by Bloch eigenvalues. We show…