zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
On the closability of classical Dirichlet forms in the plane. (English. Russian original) Zbl 1085.46023
The author exhibits a measure $\mu$ on the plane such that the Dirichlet form $E(f,g)=\int(\nabla f,\nabla g)\,d\mu$ is closable, whereas the form $E_x(f,g)=\int \partial_xf\partial_xg\,d\mu$ is not. This gives a positive answer to a question of {\it S. Albeverio} and {\it M. Röckner} [J. Funct. Anal. 88, No. 2, 395--436 (1990; Zbl 0737.46036)]. The measure $\mu$ is restriction of Lebesgue measure to an open subset of the unit square and the construction is based on a Cantor set of positive measure.

46E35Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
31C25Dirichlet spaces
46N20Applications of functional analysis to differential and integral equations
47A07Forms on topological linear spaces
47B37Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)