Comparison Principles for Subelliptic Equations of Monge-Ampère Type

Martino Bardi; Paola Mannucci

Bollettino dell'Unione Matematica Italiana (2008)

  • Volume: 1, Issue: 2, page 489-495
  • ISSN: 0392-4041

Abstract

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We present two comparison principles for viscosity sub- and supersolutions of Monge-Ampére-type equations associated to a family of vector fields. In particular, we obtain the uniqueness of a viscosity solution to the Dirichlet problem for the equation of prescribed horizontal Gauss curvature in a Carnot group.

How to cite

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Bardi, Martino, and Mannucci, Paola. "Comparison Principles for Subelliptic Equations of Monge-Ampère Type." Bollettino dell'Unione Matematica Italiana 1.2 (2008): 489-495. <http://eudml.org/doc/290456>.

@article{Bardi2008,
abstract = {We present two comparison principles for viscosity sub- and supersolutions of Monge-Ampére-type equations associated to a family of vector fields. In particular, we obtain the uniqueness of a viscosity solution to the Dirichlet problem for the equation of prescribed horizontal Gauss curvature in a Carnot group.},
author = {Bardi, Martino, Mannucci, Paola},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {489-495},
publisher = {Unione Matematica Italiana},
title = {Comparison Principles for Subelliptic Equations of Monge-Ampère Type},
url = {http://eudml.org/doc/290456},
volume = {1},
year = {2008},
}

TY - JOUR
AU - Bardi, Martino
AU - Mannucci, Paola
TI - Comparison Principles for Subelliptic Equations of Monge-Ampère Type
JO - Bollettino dell'Unione Matematica Italiana
DA - 2008/6//
PB - Unione Matematica Italiana
VL - 1
IS - 2
SP - 489
EP - 495
AB - We present two comparison principles for viscosity sub- and supersolutions of Monge-Ampére-type equations associated to a family of vector fields. In particular, we obtain the uniqueness of a viscosity solution to the Dirichlet problem for the equation of prescribed horizontal Gauss curvature in a Carnot group.
LA - eng
UR - http://eudml.org/doc/290456
ER -

References

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