In this paper we are concerned with gradient estimates for viscosity solutions of fully nonlinear second order elliptic equations, generalizing to the nonlinear setting the results of Yanyan Li and Louis Nirenberg about the so-called Glaeser estimate and improving the qualitative results contained in one of our preceding papers.
@article{BUMI_2012_9_5_2_211_0, author = {Italo Capuzzo Dolcetta and Antonio Vitolo}, title = {Pointwise Gradient Estimates of Glaeser's Type}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {5}, year = {2012}, pages = {211-224}, zbl = {1260.35029}, mrnumber = {2977245}, language = {en}, url = {http://dml.mathdoc.fr/item/BUMI_2012_9_5_2_211_0} }
Capuzzo Dolcetta, Italo; Vitolo, Antonio. Pointwise Gradient Estimates of Glaeser's Type. Bollettino dell'Unione Matematica Italiana, Tome 5 (2012) pp. 211-224. http://gdmltest.u-ga.fr/item/BUMI_2012_9_5_2_211_0/
[1] Interior a priori estimates for solutions of fully nonlinear equations, Annals of Mathematics, 130 (1989), 189-213. | MR 1005611 | Zbl 0692.35017
,[2] Fully Nonlinear Elliptic Equations, American Mathematical Society Colloquium Publications, 43 (1995), Providence, Rhode Island. | MR 1351007
- ,[3] Gradient and Hölder estimates for positive solutions of Pucci type equations, C. R., Math., Acad. Sci. Paris, 346 (2008), 527-532. | MR 2412790 | Zbl 1145.35050
- ,[4] and Glaeser type estimates, Rend. Mat., Ser VII, 29 (2009), 17-27. | MR 2548484
- ,[5] Glaeser's type gradient estimates for non- negative solutions of fully nonlinear elliptic equations, Discrete ans Continuous Dynamical Systems-Series A (DCDS-A). A special issue Dedicated to Louis Nirenberg on the Occasion of his 85th Birthday Part I, 28, n. 2 (October 2010), 539-557. | MR 2644755 | Zbl 1193.35043
- ,[6] User's guide to viscosity solutions of second order partial differential equations, Bulletin of the American Mathematical Society, 27 (1992), 1-67. | MR 1118699 | Zbl 0755.35015
- - ,[7] 224, Springer-Verlag, Berlin-New York (1983). | MR 737190 | Zbl 0562.35001
- , Elliptic Partial Differential Equations of Second Order, 2nd ed., Grundlehren der Mathematischen Wissenschaften No.[8] Racine carrée d'une fonction différentiable, Ann. Ist. Fourier, 13 (1963), 203-207. | MR 163995 | Zbl 0128.27903
,[9] Sur certaines propriétés des trajectoires en dynamique, J. Math. Sér. 5, 3 (1897), 331-387. | Zbl 28.0643.01
,[10] Une géneralization de l'inégalité de M. J. Hadamard entre les bornes supériores des dérivées successives d'une fonction, C. R. Acad. Sci. Paris, 207 (1963), 764-765.
,[11] Einige Ungleichungen für zweimal differenzierbare Funktionen, Proc. London Math. Soc., 13 (1913), 43-49. | MR 1577513 | Zbl 44.0463.02
,[12] Generalization of a well-known inequality, Progress in Nonlinear Differential Equations and Their Applications, 66 (2005), 365-370. | MR 2187814 | Zbl 1284.26021
- ,[13] Variations on the theme of the inequality , Manuscripta Math., 56 (1986), 89-104. | MR 846988 | Zbl 0605.26010
- ,[14] Sharp pointwise interpolation inequalities for derivatives, Funct. Anal. Appl., 36 (2002), 30-48. | Zbl 1034.42018
- ,