A new proof of the Gaffney's inequality for differential forms on manifolds-with-boundary: the variational approach à la Kozono--Yanagisawa
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866908794527678464 |
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| author | Li, Siran |
| author_facet | Li, Siran |
| contents | Let $(\mathcal{M},g_0)$ be a compact Riemannian manifold-with-boundary. We present a new proof of the classical Gaffney's inequality for differential forms in boundary value spaces over $\mathcal{M}$, via the variational approach à la Kozono--Yanagisawa [$L^r$-variational inequality for vector fields and the Helmholtz--Weyl decomposition in bounded domains, Indiana Univ. Math. J. 58 (2009), 1853--1920] combined with global computations based on the Bochner's technique. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_00933 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A new proof of the Gaffney's inequality for differential forms on manifolds-with-boundary: the variational approach à la Kozono--Yanagisawa Li, Siran Analysis of PDEs Differential Geometry History and Overview 58A10, 58J32 Let $(\mathcal{M},g_0)$ be a compact Riemannian manifold-with-boundary. We present a new proof of the classical Gaffney's inequality for differential forms in boundary value spaces over $\mathcal{M}$, via the variational approach à la Kozono--Yanagisawa [$L^r$-variational inequality for vector fields and the Helmholtz--Weyl decomposition in bounded domains, Indiana Univ. Math. J. 58 (2009), 1853--1920] combined with global computations based on the Bochner's technique. |
| title | A new proof of the Gaffney's inequality for differential forms on manifolds-with-boundary: the variational approach à la Kozono--Yanagisawa |
| topic | Analysis of PDEs Differential Geometry History and Overview 58A10, 58J32 |
| url | https://arxiv.org/abs/2011.00933 |