Nonlocal Quasilinear Parabolic Equations in Heisenberg Group: Local Boundedness with an Optimal Tail
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916680509161472 |
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| author | Kar, Debraj Tewary, Vivek |
| author_facet | Kar, Debraj Tewary, Vivek |
| contents | We prove local boundedness for a quasilinear parabolic equation on the Heisenberg group
\[
\partial_t u(ξ,t) + \text{p.v.}\int_{\mathbb{H}^N} \frac{|u(ξ,t)-u(η,t)|^{p-2}(u(ξ,t)-u(η,t))}{|η^{-1}\circ ξ|^{Q+sp}} \,dη= 0,
\] 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06644 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlocal Quasilinear Parabolic Equations in Heisenberg Group: Local Boundedness with an Optimal Tail Kar, Debraj Tewary, Vivek Analysis of PDEs 35B45, 35B65, 35K55, 35R11, 46E35 We prove local boundedness for a quasilinear parabolic equation on the Heisenberg group \[ \partial_t u(ξ,t) + \text{p.v.}\int_{\mathbb{H}^N} \frac{|u(ξ,t)-u(η,t)|^{p-2}(u(ξ,t)-u(η,t))}{|η^{-1}\circ ξ|^{Q+sp}} \,dη= 0, \] 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. |
| title | Nonlocal Quasilinear Parabolic Equations in Heisenberg Group: Local Boundedness with an Optimal Tail |
| topic | Analysis of PDEs 35B45, 35B65, 35K55, 35R11, 46E35 |
| url | https://arxiv.org/abs/2504.06644 |