*(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 ${\mathbb{R}}^{N}$. 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:

49J10 | Free problems in several independent variables (existence) |

49J27 | Optimal control problems in abstract spaces (existence) |

46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |