Hölder a priori estimates for second order tangential operators on CR manifolds
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[1] University of Bologna
University of Bologna
Bolonia, Italia
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- Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 2, Nº 2, 2003, págs. 345-378
- Idioma: inglés
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Resumen
On a real hypersurface M in \mathbb{C}^{n+1} of class C^{2,\alpha } we consider a local CR structure by choosing n complex vector fields W_j in the complex tangent space. Their real and imaginary parts span a 2n-dimensional subspace of the real tangent space, which has dimension 2n+1. If the Levi matrix of M is different from zero at every point, then we can generate the missing direction. Under this assumption we prove interior a priori estimates of Schauder type for solutions of a class of second order partial differential equations with C^\alpha coefficients, which are not elliptic because they involve second-order differentiation only in the directions of the real and imaginary part of the tangential operators W_j. In particular, our result applies to a class of fully nonlinear PDE’s naturally arising in the study of domains of holomorphy in the theory of holomorphic functions of several complex variables.
