34 citations · 107 across the 46 of their papers we have counts for
7 papers · 2 filters
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…
On global estimates for systems with -growth in rough domains
M. Bulíček, S. Byun, P. Kaplický +2
We study regularity results for nonlinear parabolic systems of -Laplacian type with inhomogeneous boundary and initial data, with . We show bounds o…
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 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…
Regularity Results of the Thin Obstacle Problem for the -Laplacian
Sun-sig Byun, Ki-ahm Lee, Jehan Oh +1
We study thin obstacle problems involving the energy functional with -growth. We prove higher integrability and Hölder regularity for the gradient of minimizers of the thin o…