16 papers
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 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…