15 papers · 1 filter
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<…
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…
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 -…
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…