Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0704.49006
Lions, P.-L.
The concentration-compactness principle in the calculus of variations. The limit case. II. (English)
[J] Rev. Mat. Iberoam. 1, No.2, 45-121 (1985). ISSN 0213-2230

Summary: [For part I see the author, ibid. No.1, 145-201 (1985; Zbl 0704.49005).] \par 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 ${\bbfR}\sp N$. 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 2000:: *49J10 Free problems in several independent variables (existence)
49J27 Optimal control problems in abstract spaces (existence)
46E35 Sobolev spaces and generalizations

Keywords: Sobolev inequalities; convolution or trace inequalities; concentration- compactness principle

Citations: Zbl 0704.49005

Cited in: Zbl 1166.35334 Zbl 1059.58017 Zbl 0852.35044 Zbl 0704.49005

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]