Mixed local-nonlocal $p$-Laplace equation with variable singular nonlinearity in the Heisenberg group
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908707238969344 |
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| author | Garain, Prashanta |
| author_facet | Garain, Prashanta |
| contents | We investigate a mixed local-nonlocal $p$-Laplace equation on the Heisenberg group, where the nonlinear term features a variable singular exponent. Our analysis establishes the existence, uniqueness, and regularity of weak solutions under suitable structural assumptions. To the best of our knowledge, this work provides the first treatment of such mixed local-nonlocal problems in a non-commutative setting, even in the linear case $p=2$ with a constant singular exponent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11442 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mixed local-nonlocal $p$-Laplace equation with variable singular nonlinearity in the Heisenberg group Garain, Prashanta Analysis of PDEs 35J62, 35J75, 35R03, 35R11, 35A02 We investigate a mixed local-nonlocal $p$-Laplace equation on the Heisenberg group, where the nonlinear term features a variable singular exponent. Our analysis establishes the existence, uniqueness, and regularity of weak solutions under suitable structural assumptions. To the best of our knowledge, this work provides the first treatment of such mixed local-nonlocal problems in a non-commutative setting, even in the linear case $p=2$ with a constant singular exponent. |
| title | Mixed local-nonlocal $p$-Laplace equation with variable singular nonlinearity in the Heisenberg group |
| topic | Analysis of PDEs 35J62, 35J75, 35R03, 35R11, 35A02 |
| url | https://arxiv.org/abs/2512.11442 |