On the Hölder Property of Solutions of a Generalized System of Beltrami Equations
We define a generalized Beltrami system, which is a broad generalization of the scalar Beltrami equation to vector equations. The Riemann-Hilbert boundary value problem is considered for such a system under the assumption that it is elliptic (i.e., the roots of the characteristic equation belong to...
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Veröffentlicht in: | Differential equations 2019-02, Vol.55 (2), p.231-242 |
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Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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Zusammenfassung: | We define a generalized Beltrami system, which is a broad generalization of the scalar Beltrami equation to vector equations. The Riemann-Hilbert boundary value problem is considered for such a system under the assumption that it is elliptic (i.e., the roots of the characteristic equation belong to the interior of the unit disk centered at zero). A Cordes type condition on the location of the roots of the characteristic equation of the system is obtained; this is a sufficient condition for the solution of this problem to have the Hölder property. The proof is based on the properties of singular integral operators in a domain. |
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ISSN: | 0012-2661 1608-3083 |
DOI: | 10.1134/S0012266119020083 |