zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Radial fractional Laplace operators and Hessian inequalities. (English) Zbl 06042405
MSC:
35J60Nonlinear elliptic equations
35J70Degenerate elliptic equations
References:
[1]Andrews, G. E.; Askey, R.; Roy, R.: Special functions, Encyclopedia math. Appl. 71 (1999)
[2]Bliedtner, J.; Hansen, W.: Potential theory – an analytic and probabilistic approach to balayage, Universitext (1986) · Zbl 0706.31001
[3]Caffarelli, L.; Silvestre, L.: An extension problem related to the fractional Laplacian, Commun. partial differ. Equ. 32, 1245-1260 (2007) · Zbl 1143.26002 · doi:10.1080/03605300600987306
[4]Ferrari, F.: Ground state solutions for k-th Hessian operators, Boll. unione mat. Ital. B (7) 9, 553-586 (1995) · Zbl 0854.35034
[5]F. Ferrari, B. Franchi, I. Verbitsky, Hessian inequalities and the fractional Laplacian, J. Reine Angew. Math. (Crelle’s Journal), http://dx.doi.org/10.1515/crelle.2011.116, in press.
[6]Hardy, G. H.; Littlewood, J. E.; Polya, G.: Inequalities, (1934) · Zbl 0010.10703
[7]Hartman, P.: Ordinary differential equations, (2002)
[8]Karp, D.; Sitnik, S. M.: Inequalities and monotonicity of ratios of hypergeometric like functions, J. approx. Theory 161, 337-352 (2009) · Zbl 1185.33008 · doi:10.1016/j.jat.2008.10.002
[9]Karp, D.; Sitnik, S. M.: Log-convexity and log-concavity for generalized hypergeometric functions, J. math. Anal. appl. 364, 384-394 (2010) · Zbl 1226.33003 · doi:10.1016/j.jmaa.2009.10.057
[10]Landkof, N. S.: Foundations of modern potential theory, Grundlehren math. Wiss. 180 (1972) · Zbl 0253.31001
[11]Magnus, W.; Oberhettinger, F.; Soni, R. P.: Formulas and theorems for the special functions of mathematical physics, Grundlehren math. Wiss. 52 (1966) · Zbl 0143.08502
[12]Trudinger, N. S.; Wang, X. -J.: Hessian measures I, Topol. methods nonlinear anal. 10, 225-239 (1997)
[13]Trudinger, N. S.; Wang, X. -J.: Hessian measures II, Ann. math. 150, 579-604 (1999) · Zbl 0947.35055 · doi:10.2307/121089 · doi:http://www.math.princeton.edu/~annals/issues/1999/150_2.html
[14]Verbitsky, I. E.: Hessian Sobolev and Poincaré inequalities, Math. forschungsinst. Oberwolfach 36, 33-35 (2011)
[15]Wang, X. -J.: A class of fully nonlinear elliptic equations and related functionals, Indiana univ. Math. J. 43, 25-54 (1994) · Zbl 0805.35036 · doi:10.1512/iumj.1994.43.43002
[16]Wang, X. -J.: The k-Hessian equation, Lecture notes in math. 1977 (2009)