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math.AP2025
Hölder regularity of doubly nonlinear nonlocal quasilinear parabolic equations in some mixed singular-degenerate regime
Karthik Adimurthi, Mitesh Modasiya
We study local Hölder regularity of bounded, weak solutions for the nonlocal quasilinear equations of the form \[ (|u|^{q-2}u)_t + \text{P.V.} \int_{\mathbb{R}^n} \frac{|u(x,t) -…
math.AP2025
Local Hölder regularity for bounded, signed solutions to nonlocal Trudinger equations
Karthik Adimurthi
We prove local Hölder regularity for bounded and sign-changing weak solutions to nonlocal Trudinger equations of the form \[ (|u|^{p-2}u)_t + \text{P.V.} \int_{\mathbb{R}^n} \frac…
math.AP2024
Gradient regularity for mixed local-nonlocal quasilinear parabolic equations
Karthik Adimurthi, Harsh Prasad, Vivek Tewary
In this paper, we prove local Hölder continuity for the spatial gradient of weak solutions to $$u_t - \text{div} (|\nabla u|^{p-2}\nabla u) + \text{P.V.} \int_{\mathbb{R}^n} \frac…