[Principes du maximum et inégalités isopérimétriques pour certains problèmes du type Monge–Ampère]
Dans cette note, nous obtenons un principe du maximum pour une combinaison fonctionnelle appropriée de et , où est une solution classique strictement convexe à une classe générale dʼéquations du type Monge–Ampère. Ce principe du maximum est ensuite utilisé pour établir certaines inégalités isopérimétriques dʼintérêt dans la théorie de surfaces de courbure de Gauss constante dans .
In this note we derive a maximum principle for an appropriate functional combination of and , where is a strictly convex classical solution to a general class of Monge–Ampère equations. This maximum principle is then employed to establish some isoperimetric inequalities of interest in the theory of surfaces of constant Gauss curvature in .
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@article{CRMATH_2014__352_1_37_0,
author = {Enache, Cristian},
title = {Maximum principles and isoperimetric inequalities for some {Monge{\textendash}Amp\`ere-type} problems},
journal = {Comptes Rendus. Math\'ematique},
pages = {37--42},
publisher = {Elsevier},
volume = {352},
number = {1},
year = {2014},
doi = {10.1016/j.crma.2013.10.035},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2013.10.035/}
}
TY - JOUR AU - Enache, Cristian TI - Maximum principles and isoperimetric inequalities for some Monge–Ampère-type problems JO - Comptes Rendus. Mathématique PY - 2014 SP - 37 EP - 42 VL - 352 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2013.10.035/ DO - 10.1016/j.crma.2013.10.035 LA - en ID - CRMATH_2014__352_1_37_0 ER -
%0 Journal Article %A Enache, Cristian %T Maximum principles and isoperimetric inequalities for some Monge–Ampère-type problems %J Comptes Rendus. Mathématique %D 2014 %P 37-42 %V 352 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2013.10.035/ %R 10.1016/j.crma.2013.10.035 %G en %F CRMATH_2014__352_1_37_0
Enache, Cristian. Maximum principles and isoperimetric inequalities for some Monge–Ampère-type problems. Comptes Rendus. Mathématique, Tome 352 (2014) no. 1, pp. 37-42. doi : 10.1016/j.crma.2013.10.035. http://www.numdam.org/articles/10.1016/j.crma.2013.10.035/
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