Let 1<∞. In this article we establish an L^p-Hodge decomposition theorem on sub-Riemannian compact contact manifolds without boundary, related to the Rumin complex of differential forms. Given an Lp- Rumin's form, we adopt an approach in the spirit of Morrey's book [26] (further performed in [18]) to obtain a decomposition with higher regular “primitives” i.e. that belong to suitable Sobolev classes. Our proof relies on recent results obtained in [4] and [6].
Baldi, A., Rosa, A. (2025). L^p-Hodge decomposition with Sobolev classes in sub-Riemannian contact manifolds. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 552(1), 1-36 [10.1016/j.jmaa.2025.129739].
L^p-Hodge decomposition with Sobolev classes in sub-Riemannian contact manifolds
Baldi, Annalisa
;
2025
Abstract
Let 1<∞. In this article we establish an L^p-Hodge decomposition theorem on sub-Riemannian compact contact manifolds without boundary, related to the Rumin complex of differential forms. Given an Lp- Rumin's form, we adopt an approach in the spirit of Morrey's book [26] (further performed in [18]) to obtain a decomposition with higher regular “primitives” i.e. that belong to suitable Sobolev classes. Our proof relies on recent results obtained in [4] and [6].| File | Dimensione | Formato | |
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