[Estimations Hölder et du gradient pour les solutions non négatives des équations de Pucci]
Le but de cette Note est de donner des estimations pour les solutions de viscosité non négatives d'une classe d'équations complètement non linéaires comprenante les équations extrémales de Pucci, en généralisant ainsi des résultats récents dues à Y.Y. Li et L. Nirenberg.
We present some estimates for positive viscosity solutions of a class of fully non-linear elliptic equations including the extremal Pucci equations, generalizing some results for linear equations recently established by Y.Y. Li and L. Nirenberg.
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@article{CRMATH_2008__346_9-10_527_0,
author = {Capuzzo Dolcetta, Italo and Vitolo, Antonio},
title = {Gradient and {H\"older} estimates for positive solutions of {Pucci} type equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {527--532},
publisher = {Elsevier},
volume = {346},
number = {9-10},
year = {2008},
doi = {10.1016/j.crma.2008.03.004},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2008.03.004/}
}
TY - JOUR AU - Capuzzo Dolcetta, Italo AU - Vitolo, Antonio TI - Gradient and Hölder estimates for positive solutions of Pucci type equations JO - Comptes Rendus. Mathématique PY - 2008 SP - 527 EP - 532 VL - 346 IS - 9-10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2008.03.004/ DO - 10.1016/j.crma.2008.03.004 LA - en ID - CRMATH_2008__346_9-10_527_0 ER -
%0 Journal Article %A Capuzzo Dolcetta, Italo %A Vitolo, Antonio %T Gradient and Hölder estimates for positive solutions of Pucci type equations %J Comptes Rendus. Mathématique %D 2008 %P 527-532 %V 346 %N 9-10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2008.03.004/ %R 10.1016/j.crma.2008.03.004 %G en %F CRMATH_2008__346_9-10_527_0
Capuzzo Dolcetta, Italo; Vitolo, Antonio. Gradient and Hölder estimates for positive solutions of Pucci type equations. Comptes Rendus. Mathématique, Tome 346 (2008) no. 9-10, pp. 527-532. doi : 10.1016/j.crma.2008.03.004. http://www.numdam.org/articles/10.1016/j.crma.2008.03.004/
[1] Interior regularity theory for a class of nonconvex fully nonlinear elliptic equations, J. Math. Pures Appl. (9), Volume 82 (2003) no. 5, pp. 573-612
[2] Interior a priori estimates for solutions of fully nonlinear equations, Ann. of Math., Volume 130 (1989), pp. 189-213
[3] Fully Nonlinear Elliptic Equations, American Mathematical Society Colloquium Publications, vol. 43, American Mathematical Society, Providence, RI, 1995
[4] User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc., Volume 27 (1992) no. 1, pp. 1-67
[5] Classical solutions of fully nonlinear, convex, second-order elliptic equations, Comm. Pure Appl. Math., Volume 25 (1982), pp. 333-363
[6] Elliptic Partial Differential Equations of Second Order, Grundlehren der Mathematischen Wissenschaften, vol. 224, Springer-Verlag, Berlin, New York, 1983
[7] Viscosity solutions of fully nonlinear second order elliptic partial differential equations, J. Differential Equations, Volume 83 (1990), pp. 26-78
[8] Generalization of a well-known inequality, Progress in Nonlinear Differential Equations and Their Applications, vol. 66, 2005, pp. 365-370
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