Lipschitz regularity for solutions to an orthotropic $q$-Laplacian-type equation in the Heisenberg group
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915738488406016 |
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| author | Circelli, Michele Citti, Giovanna Clop, Albert |
| author_facet | Circelli, Michele Citti, Giovanna Clop, Albert |
| contents | We establish the local Lipschitz regularity for solutions to an orthotropic q-Laplacian-type equation within the Heisenberg group. Our approach is largely inspired by the works of X. Zhong, who investigated the q-Laplacian in the same setting and proved the Hölder regularity for the gradient of solutions. Due to the degeneracy of the current equation, such regularity for the gradient of solutions is not even known in the Euclidean setting for dimensions greater than 2, where only boundedness is expected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07548 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lipschitz regularity for solutions to an orthotropic $q$-Laplacian-type equation in the Heisenberg group Circelli, Michele Citti, Giovanna Clop, Albert Analysis of PDEs We establish the local Lipschitz regularity for solutions to an orthotropic q-Laplacian-type equation within the Heisenberg group. Our approach is largely inspired by the works of X. Zhong, who investigated the q-Laplacian in the same setting and proved the Hölder regularity for the gradient of solutions. Due to the degeneracy of the current equation, such regularity for the gradient of solutions is not even known in the Euclidean setting for dimensions greater than 2, where only boundedness is expected. |
| title | Lipschitz regularity for solutions to an orthotropic $q$-Laplacian-type equation in the Heisenberg group |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.07548 |