Coerciveness and Morrey Inequalities for Elliptic Operators with Natural Boundary Conditions via Weitzenböck Identities
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913315433742336 |
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| author | Duse, Erik Rosén, Andreas |
| author_facet | Duse, Erik Rosén, Andreas |
| contents | We prove a Weitzenböck identity for general pairs of constant coefficient homogeneous first order partial differential operators, and deduce from it sufficient algebraic conditions for coerciveness and Morrey estimates under the natural 1/2 boundary conditions. Our proof of the $W^{1,2}$ elliptic estimate relies on the Aronszajn-Necas-Smith coercive estimate. For generalized strongly pseudoconvex domains, we improve the Morrey estimate to a weighted $W^{1,2}$ square function estimate, using a generalized Cauchy-Pompieu reproducing formula and the T1 theorem for singular integrals. We use Van Schaftingen's notion of cocanceling to study the generalized Levi forms appearing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09628 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coerciveness and Morrey Inequalities for Elliptic Operators with Natural Boundary Conditions via Weitzenböck Identities Duse, Erik Rosén, Andreas Analysis of PDEs We prove a Weitzenböck identity for general pairs of constant coefficient homogeneous first order partial differential operators, and deduce from it sufficient algebraic conditions for coerciveness and Morrey estimates under the natural 1/2 boundary conditions. Our proof of the $W^{1,2}$ elliptic estimate relies on the Aronszajn-Necas-Smith coercive estimate. For generalized strongly pseudoconvex domains, we improve the Morrey estimate to a weighted $W^{1,2}$ square function estimate, using a generalized Cauchy-Pompieu reproducing formula and the T1 theorem for singular integrals. We use Van Schaftingen's notion of cocanceling to study the generalized Levi forms appearing. |
| title | Coerciveness and Morrey Inequalities for Elliptic Operators with Natural Boundary Conditions via Weitzenböck Identities |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.09628 |