The concentration-compactness principle in the calculus of variations. The locally compact case, part 2
The concentration-compactness principle in the calculus of variations. The limit case, Part II.
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 non-compact group of transformations like the dilations in RN. This contains for example the class of problems associated with the determination of extremal functions in inequalities like Sobolev inequalities, convolution or trace inequalities... We show how the concentration-compactness principle and method...
The concentration-compactness principle in the calculus of variations. The limit case, Part I.
After the study made in the locally compact case for variational problems with some translation invariance, we investigate here the variational problems (with constraints) for example in RN where the invariance of RN by the group of dilatations creates some possible loss of compactness. This is for example the case for all the problems associated with the determination of extremal functions in functional inequalities (like for example the Sobolev inequalities). We show here how the concentration-compactness...
The Monge problem on non-compact manifolds
The Mumford-Shah conjecture in image processing
The relaxed energy for -valued maps and measurable weights
The structure of extremals of a class of second order variational problems
Two-dimensional examples of rank-one convex functions that are not quasiconvex
The aim of this note is to provide two-dimensional examples of rank-one convex functions which are not quasiconvex.
Two-dimensional Newton's problem of minimal resistance
Two-dimensional stable Lavrentiev phenomenon with and without boundary conditions