Weak Differentiability to Nonuniform Nonlinear Degenerate Elliptic Systems under $p,q$-growth Condition on the Heisenberg Group
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866908820906704896 |
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| author | Zhang, Junli Li, Zhouyu |
| author_facet | Zhang, Junli Li, Zhouyu |
| contents | The paper concerns the weak differentiability of weak solutions to two kinds of nonuniform nonlinear degenerate elliptic systems under the $p,q$-growth condition on the Heisenberg Group. We use the iteration to fractional difference quotients on the Heisenberg Group to get the weak differentiability of weak solution $u$ in the vertical direction (i.e., ${L^p}$($1<p<4$) integrability of $Tu$) and then the second order weak differentiability of weak solution in the horizontal directions (i.e., ${L^2}$ integrability of $\nabla_H^2u$) and weak differentiability of gradient of weak solution in the vertical direction (i.e., ${L^2}$ integrability of $T{\nabla_H}u$)). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_02320 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Weak Differentiability to Nonuniform Nonlinear Degenerate Elliptic Systems under $p,q$-growth Condition on the Heisenberg Group Zhang, Junli Li, Zhouyu Analysis of PDEs 35H20, 35B65, 35J60, 35J70 The paper concerns the weak differentiability of weak solutions to two kinds of nonuniform nonlinear degenerate elliptic systems under the $p,q$-growth condition on the Heisenberg Group. We use the iteration to fractional difference quotients on the Heisenberg Group to get the weak differentiability of weak solution $u$ in the vertical direction (i.e., ${L^p}$($1<p<4$) integrability of $Tu$) and then the second order weak differentiability of weak solution in the horizontal directions (i.e., ${L^2}$ integrability of $\nabla_H^2u$) and weak differentiability of gradient of weak solution in the vertical direction (i.e., ${L^2}$ integrability of $T{\nabla_H}u$)). |
| title | Weak Differentiability to Nonuniform Nonlinear Degenerate Elliptic Systems under $p,q$-growth Condition on the Heisenberg Group |
| topic | Analysis of PDEs 35H20, 35B65, 35J60, 35J70 |
| url | https://arxiv.org/abs/2302.02320 |