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)
The concentration-compactness principle in the calculus of variations. The limit case. II. (English) Zbl 0704.49006

Summary: [For part I see the author, ibid. No.1, 145-201 (1985; Zbl 0704.49005).]

This paper is the second part of a work devoted to the study of variational problems (with constraints) in functional spaces defined on domains presenting some (local) form of invariance by a noncompact group of transformations like the dilations in N . This contains, for example, the class of problems associated with the determination of extremal functions in inequalities such as Sobolev inequalities, convolution or trace inequalities. We show how the concentration- compactness principle and method introduced in the so-called locally compact case are to be modified in order to solve these problems, and we present applications to functional analysis, mathematical physics, differential geometry and harmonic analysis.


MSC:
49J10Free problems in several independent variables (existence)
49J27Optimal control problems in abstract spaces (existence)
46E35Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems