Hölder a priori estimates for second order tangential operators on CR manifolds
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 2 (2003) no. 2, p. 345-378

On a real hypersurface $M$ in ${ℂ}^{n+1}$ 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.

Classification:  35J70,  35H20,  32W50,  22E30
@article{ASNSP_2003_5_2_2_345_0,
author = {Montanari, Annamaria},
title = {H\"older a priori estimates for second order tangential operators on CR manifolds},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola normale superiore},
volume = {Ser. 5, 2},
number = {2},
year = {2003},
pages = {345-378},
zbl = {1170.35433},
mrnumber = {2005607},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2003_5_2_2_345_0}
}

Montanari, Annamaria. Hölder a priori estimates for second order tangential operators on CR manifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 2 (2003) no. 2, pp. 345-378. http://www.numdam.org/item/ASNSP_2003_5_2_2_345_0/

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