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Minimizers of energy functionals under not very integrable contraints. (English) Zbl 1052.49017
From the introduction: “In this article, we characterize the solutions to a general problem of minimization of an energy functional under “bad” linear constraints. This badness is a consequence of a lack of integrability of the moment function defining the constraint. As a consequence, the minimizers may exhibit a singular component. This characterization is obtained without assuming any constraint qualification for a general linear constraint”.

49J45 Methods involving semicontinuity and convergence; relaxation
52A41 Convex functions and convex programs in convex geometry
90C25 Convex programming
49N15 Duality theory (optimization)