Abstract
Publisher Summary This chapter discusses the variational problems with singular solutions. Variational problems that are coercive on a nonreflexive Banach space may possess singular solutions. Singular variational problems of this type arise in mechanics and physics—that is, in solid mechanics or in problems related to minimal area surfaces or to surfaces of given mean curvature. The chapter presents two examples of variational problems in the calculus of variations with singular solutions, one of them is related to minimal surfaces, and other one is a problem encountered in plasticity. The chapter also discusses the convex function of a measure, time dependent minimal surfaces, and a problem in the plasticity of plates.
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