Capuzzo Dolcetta, Italo and Vitolo, Antonio:
Pointwise Gradient Estimates of Glaeser's Type
Bollettino dell'Unione Matematica Italiana Serie 9 5 (2012), fasc. n.2, p. 211-224, (English)
pdf (293 Kb), djvu (123 Kb). | MR 2977245 | Zbl 1260.35029
Sunto
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.
Referenze Bibliografiche
[2]
L. A. CAFFARELLI -
X. CABRÈ ,
Fully Nonlinear Elliptic Equations,
American Mathematical Society Colloquium Publications,
43 (
1995), Providence, Rhode Island. |
fulltext (doi) |
MR 1351007[3]
I. CAPUZZO DOLCETTA -
A. VITOLO,
Gradient and Hölder estimates for positive solutions of Pucci type equations,
C. R., Math., Acad. Sci. Paris,
346 (
2008), 527-532. |
fulltext (doi) |
MR 2412790 |
Zbl 1145.35050[4]
I. CAPUZZO DOLCETTA -
A. VITOLO,
$C^{1,\alpha}$ and Glaeser type estimates,
Rend. Mat., Ser VII,
29 (
2009), 17-27. |
MR 2548484[5]
I. CAPUZZO DOLCETTA -
A. VITOLO,
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. |
fulltext (doi) |
MR 2644755 |
Zbl 1193.35043[6]
M. G. CRANDALL -
H. ISHII -
P. L. LIONS,
User's guide to viscosity solutions of second order partial differential equations,
Bulletin of the American Mathematical Society,
27 (
1992), 1-67. |
fulltext (doi) |
MR 1118699 |
Zbl 0755.35015[7]
D. GILBARG -
N. S. TRUDINGER,
Elliptic Partial Differential Equations of Second Order, 2nd ed.,
Grundlehren der Mathematischen Wissenschaften No.
224,
Springer-Verlag, Berlin-New York (
1983). |
fulltext (doi) |
MR 737190 |
Zbl 0562.35001[9]
J. HADAMARD,
Sur certaines propriétés des trajectoires en dynamique,
J. Math. Sér. 5,
3 (
1897), 331-387. |
fulltext EuDML |
Zbl 28.0643.01[10] A. N. KOLMOGOROV, 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.
[12]
Y. Y. LI -
L. NIRENBERG,
Generalization of a well-known inequality,
Progress in Nonlinear Differential Equations and Their Applications,
66 (
2005), 365-370. |
fulltext (doi) |
MR 2187814 |
Zbl 1284.26021[13]
V. G. MAZ'YA -
A. KUFNER,
Variations on the theme of the inequality $(f')^2 \leq 2f \sup |f''|$,
Manuscripta Math.,
56 (
1986), 89-104. |
fulltext (doi) |
MR 846988 |
Zbl 0605.26010[14]
V. G. MAZ'YA -
T. O. SHAPOSHNIKOVA,
Sharp pointwise interpolation inequalities for derivatives,
Funct. Anal. Appl.,
36 (
2002), 30-48. |
Zbl 1034.42018