Hölder a priori estimates for second order tangential operators on CR manifolds

Annamaria Montanari

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2003)

  • Volume: 2, Issue: 2, page 345-378
  • ISSN: 0391-173X

Abstract

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On a real hypersurface M in ℂ n + 1 of class C 2 , α 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 2 n -dimensional subspace of the real tangent space, which has dimension 2 n + 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 α 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.

How to cite

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Montanari, Annamaria. "Hölder a priori estimates for second order tangential operators on CR manifolds." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 2.2 (2003): 345-378. <http://eudml.org/doc/84504>.

@article{Montanari2003,
abstract = {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.},
author = {Montanari, Annamaria},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {2},
pages = {345-378},
publisher = {Scuola normale superiore},
title = {Hölder a priori estimates for second order tangential operators on CR manifolds},
url = {http://eudml.org/doc/84504},
volume = {2},
year = {2003},
}

TY - JOUR
AU - Montanari, Annamaria
TI - Hölder a priori estimates for second order tangential operators on CR manifolds
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2003
PB - Scuola normale superiore
VL - 2
IS - 2
SP - 345
EP - 378
AB - 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.
LA - eng
UR - http://eudml.org/doc/84504
ER -

References

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