Anzeige
Erschienen in:
2012 | OriginalPaper | Buchkapitel
Hierarchical Construction of Bounded Solutions of div U=F in Critical Regularity Spaces
verfasst von : Eitan Tadmor, Changhui Tan
Erschienen in: Nonlinear Partial Differential Equations
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Abstract
We implement the hierarchical decomposition introduced in (Tadmor in Hierarchical construction of bounded solutions in critical regularity spaces, arXiv:1003.1525v2), to construct uniformly bounded solutions of the problem div U=F, where the two-dimensional data is in the critical regularity space, \(F\in L^{2}_{\#}(\mathbb{T}^{2})\). Criticality in this context, manifests itself by the lack of linear mapping, \(F\in L^{2}_{\#}(\mathbb{T}^{2})\mapsto U\in L^{\infty}(\mathbb{T}^{2})\), (Bourgain and Brezis in J. Am. Math. Soc. 16(2):393–426, 2003). Thus, the intriguing aspect here is that although the problem is linear, the construction of its uniformly bounded solutions is not.