8 citations · 17 across the 28 of their papers we have counts for
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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…
Boundary higher integrability for very weak solutions of quasilinear parabolic equations
Karthik Adimurthi, Sun-Sig Byun
We prove boundary higher integrability for the (spatial) gradient of \emph{very weak} solutions of quasilinear parabolic equations of the form $$u_t - \text{div}\,\mathcal{A}(x,t,…
Interior and boundary higher integrability of very weak solutions for quasilinear parabolic equations with variable exponents
Karthik Adimurthi, Sun-Sig Byun, Jehan Oh
We prove boundary higher integrability for the (spatial) gradient of \emph{very weak} solutions of quasilinear parabolic equations of the form $$ \left\{ \begin{array}{ll} u_t - di…