Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0943.49012
Sychev, M.A.
A new approach to Young measure theory, relaxation and convergence in energy. (English)
[J] Ann. Inst. Henri Poincaré, Anal. Non Linéaire 16, No.6, 773-812 (1999). ISSN 0294-1449

The paper contains a detailed presentation of the theory of Young measures, with particular emphasis on their application to the study of lower semicontinuity of integral functionals of the calculus of variations of the form $$I(u)= \int_\Omega L(x,u,\nabla u) dx.\tag 1$$ Section 2 deals with some properties of functions in Sobolev spaces. Section 3 is devoted to Young measures and to the characterization of them as measurable functions into a suitable metric space. In Section 4 the theory of gradient Young measures is presented together with a survey on the already existing literature. Section 5 finally deals with some applications of Young measures to the study of the asymptotic behaviour of integral functionals of the form (1) on weakly convergent sequences of Sobolev functions, which allows to obtain relaxation results under minimal assumptions on the integrand $L$.
[G.Buttazzo (Pisa)]

MSC 2000:: *49J45 Optimal control problems inv. semicontinuity and convergence
46E35 Sobolev spaces and generalizations
35J20 Second order elliptic equations, variational methods
46E27 Spaces of measures
34B20 Weyl theory and its generalizations

Keywords: Young measures; lower semicontinuity; integral functionals; relaxation

Cited in: Zbl 1095.49014

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

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

Simple Search

Zentralblatt MATH Berlin [Germany]