Alessandro Musesti

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We extend a celebrated identity by P. Pucci and J. Serrin, concerning C 2 solutions of Euler equations of functionals of the calculus of variations, to the case of C 1 solutions under the only additional assumption of strict convexity in the gradient. Some particular cases in which the mere convexity is sufficient are also considered.
Cauchy interactions between subbodies of a continuous body are introduced in the framework of Measure Theory, extending the class of previously admissible ones. A decomposition theorem into a volume and a surface interaction is proved, as well as characterizations of the single components. Finally, an extension result and a generalized balance law are given.
By means of balanced virtual powers, an axiomatic approach is developed, in the spirit of Noll, to second-gradient continua. The measure-theoretical formulation allows a considerable simplification since the existence of an edge stress density is regarded as a special case of a surface stress which is a singular measure with respect to the area. To prove(More)
By means of a perturbation argument devised by P. Bolle, we prove the existence of infinitely many solutions for perturbed symmetric polyharmonic problems with non–homogeneous Dirichlet boundary conditions. An extension to the higher order case of the estimate from below for the critical values due to K. Tanaka is obtained.