8 citations · 17 across the 28 of their papers we have counts for
29 papers
Hölder regularity of doubly nonlinear nonlocal quasilinear parabolic equations in some mixed singular-degenerate regime
Karthik Adimurthi, Mitesh Modasiya
We study local Hölder regularity of bounded, weak solutions for the nonlocal quasilinear equations of the form \[ (|u|^{q-2}u)_t + \text{P.V.} \int_{\mathbb{R}^n} \frac{|u(x,t) - u…
Local Hölder regularity for bounded, signed solutions to nonlocal Trudinger equations
Karthik Adimurthi
We prove local Hölder regularity for bounded and sign-changing weak solutions to nonlocal Trudinger equations of the form \[ (|u|^{p-2}u)_t + \text{P.V.} \int_{\mathbb{R}^n} \frac{…
A note on Hölder regularity of weak solutions to linear elliptic equations
Karthik Adimurthi
In this paper, we show that weak solutions of $$-\text{div} \mathbb{A}(x)\nabla u = 0 \qquad \text{where}\quad \mathbb{A}(x)= \mathbb{A}(x)^T \,\, \text{and} \,\, λ|ζ|^2 \leq \lang…
Borderline gradient regularity estimates for quasilinear parabolic systems with data independent of time
Karthik Adimurthi, Wontae Kim
In this paper, we study some regularity issues concerning the gradient of weak solutions of , where is mo…
Gradient regularity for mixed local-nonlocal quasilinear parabolic equations
Karthik Adimurthi, Harsh Prasad, Vivek Tewary
In this paper, we prove local Hölder continuity for the spatial gradient of weak solutions to $$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 $$…
Local Hölder regularity for nonlocal parabolic -Laplace equations
Karthik Adimurthi, Harsh Prasad, Vivek Tewary
We prove local Hölder regularity for a nonlocal parabolic equations of the form \begin{align*} \partial_t u + \text{P.V.}\int_{\mathbb{R}^N} \frac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,…
Borderline Lipschitz regularity for bounded minimizers of functionals with (p,q)-growth
Karthik Adimurthi, Vivek Tewary
We prove local Lipschitz regularity for bounded minimizers of functionals with nonstandard -growth with the source term in the Lorentz space under the restriction $q<…
Hölder regularity for fractional -Laplace equations
Karthik Adimurthi, Harsh Prasad, Vivek Tewary
We give an alternative proof for Hölder regularity for weak solutions of nonlocal elliptic quasilinear equations modelled on the fractional p-Laplacian where we replace the discret…
Hölder regularity for anisotropic -Laplace equation
Karthik Adimurthi
In this paper, we obtain local Hölder regularity for bounded, weak solutions to the anisotropic -Laplace equation whose prototype structure is given by $$ \sum_{i=1}^N (|u_{x_i}…
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…
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…
Unified approach to regularity for quasilinear parabolic equations
Karthik Adimurthi, Agnid Banerjee
In this paper, we are interested in obtaining a unified approach for estimates for weak solutions of quasilinear parabolic equations, the prototype example being \[ u_t -…
Hölder regularity for quasilinear parabolic equations with anisotropic -Laplace nonlinearity -- Announcement
Karthik Adimurthi
We announce some new results for proving Hölder continuity of weak solutions to quasilinear parabolic equations whose prototype takes the form $$u_t - div (|\nabla u|^{p-2}\nabla u…
Twice differentiability of solutions to fully nonlinear parabolic equations near the boundary
Karthik Adimurthi, Agnid Banerjee, Ram Baran Verma
In this paper, we prove regularity for viscosity solutions to non-convex fully nonlinear parabolic equations near the boundary. This constitutes the parabolic c…
An existence result for nonhomogeneous quasilinear parabolic equations beyond the duality pairing
Karthik Adimurthi, Sun-Sig Byun, Wontae Kim
In this paper, we prove existence of \emph{very weak solutions} to nonhomogeneous quasilinear parabolic equations beyond the duality pairing. The main ingredients are a priori esit…
Uniform boundedness for weak solutions of quasilinear parabolic equations
Karthik Adimurthi, Sukjung Hwang
In this paper, we study the boundedness of weak solutions to quasilinear parabolic equations of the form \[u_t - \text{div} \mathcal{A}(x,t,\nabla u) = 0, \] where the nonlinearity…
Partial existence result for Homogeneous Quasilinear parabolic problems beyond the duality pairing
Karthik Adimurthi, Sun-Sig Byun, Wontae Kim
In this paper, we study the existence of distributional solutions solving \cref{main-3} on a bounded domain satisfying a uniform capacity density condition where the nonlinear…
Borderline regularity for fully nonlinear equations in Dini domains
Karthik Adimurthi, Agnid Banerjee
In this paper, we prove borderline gradient continuity of viscosity solutions to Fully nonlinear elliptic equations at the boundary of a $C^{1,\dini}$-domain. Our main result Theor…
End point gradient estimates for quasilinear parabolic equations with variable exponent growth on nonsmooth domains
Karthik Adimurthi, Sun-Sig Byun, Jung-Tae Park
In this paper, we study quasilinear parabolic equations with the nonlinearity structure modeled after the -Laplacian on nonsmooth domains. The main goal is to obtain end po…
Gradient weighted norm inequalities for linear elliptic equations with discontinuous coefficients
Karthik Adimurthi, Tadele Mengesha, Nguyen Cong Phuc
Local and global weighted norm estimates involving Muckenhoupt weights are obtained for gradient of solutions to linear elliptic Dirichlet boundary value problems in divergence for…
Nonlinear equations with gradient natural growth and distributional data, with applications to a Schrödinger type equation
Karthik Adimurthi, Nguyen Cong Phuc
We obtain necessary and sufficient conditions with sharp constants on the distribution for the existence of a globally finite energy solution to the quasilinear equation with a…
Quasilinear equations with natural growth in the gradients in spaces of Sobolev multipliers
Karthik Adimurthi, Nguyen Cong Phuc
We study the existence problem for a class of nonlinear elliptic equations whose prototype is of the form in a bounded domain . H…
Gradient weighted estimates at the natural exponent for Quasilinear Parabolic equations
Karthik Adimurthi, Sun-Sig Byun
In this paper, we obtain weighted norm inequalities for the spatial gradients of weak solutions to quasilinear parabolic equations with weights in the Muckenhoupt class $A_{\frac{q…