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arXiv · 2504.06644

Nonlocal Quasilinear Parabolic Equations in Heisenberg Group: Local Boundedness with an Optimal Tail

Debraj Kar·Vivek Tewary
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Abstract

We prove local boundedness for a quasilinear parabolic equation on the Heisenberg group \[ \partial_t u(\xi,t) + \text{p.v.}\int_{\mathbb{H}^N} \frac{|u(\xi,t)-u(\eta,t)|^{p-2}(u(\xi,t)-u(\eta,t))}{|\eta^{-1}\circ \xi|^{Q+sp}} \,d\eta = 0, \] 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.

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Debraj Kar, Vivek Tewary. 2025-04-09. Nonlocal Quasilinear Parabolic Equations in Heisenberg Group: Local Boundedness with an Optimal Tail. https://arxiv.org/abs/2504.06644

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