Nonlocal quasilinear parabolic equations in Heisenberg group: Local boundedness with an optimal tail
Abstract
We prove local boundedness for a quasilinear parabolic equation on the Heisenberg group$ \partial_t u(\xi, t) + \text{p.v.}\int_{ {\mathbb{H}^{\text{N}}}} \frac{|u(\xi, t)-u(\eta, t)|^{p-2}(u(\xi, t)-u(\eta, t))}{|\eta^{-1}\circ \xi|_ {\mathbb{H}^{\text{N}}}^{Q+sp}} \, d\eta = 0, $with optimal regularity assumption on the tail term. We also prove interpolation inequalities and an extension theorem for fractional Sobolev spaces on the Heisenberg group.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Differential Equations and Boundary Problems
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems
- Volume
- 51
- Issue
- 0
- Pages
- 46–95
- Publication date
- 1 January 2026