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math.AP2019
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…
math.AP2019
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…
math.AP2019
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…