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)
Estimates on Green functions and Poisson kernels for symmetric stable processes. (English) Zbl 0918.60068
Summary: We give lower and upper bound estimates for Green functions and Poisson kernels of a symmetric α-stable process X in bounded C 1,1 domains in n , where 0<α<2 and n2. An exact formula expressing the Poisson kernel of X on an arbitrary bounded domain D satisfying uniform exterior cone condition in terms of the Green function of X in D is derived. As examples of applications of these estimates, we prove that the 3G Theorem holds for X on bounded C 1,1 domains and that the conditional lifetimes for X in a bounded C 1,1 domain are uniformly bounded. A simple proof of the boundary Harnack principle for nonnegative functions which are harmonic in a bounded C 1,1 domain D with respect to the symmetric stable process is also given.

MSC:
60J99Markov processes
60J45Probabilistic potential theory
60J75Jump processes
31C99Generalizations in potential theory