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Weak and strong density results for the Dirichlet energy

Mariano Giaquinta, Domenico Mucci (2004)

Journal of the European Mathematical Society

Let 𝒴 be a smooth oriented Riemannian manifold which is compact, connected, without boundary and with second homology group without torsion. In this paper we characterize the sequential weak closure of smooth graphs in B n × 𝒴 with equibounded Dirichlet energies, B n being the unit ball in ℝ n . More precisely, weak limits of graphs of smooth maps u k : B n → 𝒴 with equibounded Dirichlet integral give rise to elements of the space cart 2 , 1 ( B n × 𝒴 ) (cf. [4], [5], [6]). In this paper we prove that every element T in cart 2 , 1 ( B n × 𝒴 ) is the weak limit...

Weight minimization of elastic bodies weakly supporting tension. I. Domains with one curved side

Ivan Hlaváček, Michal Křížek (1992)

Applications of Mathematics

Shape optimization of a two-dimensional elastic body is considered, provided the material is weakly supporting tension. The problem generalizes that of a masonry dam subjected to its own weight and to the hydrostatic presure. Existence of an optimal shape is proved. Using a penalty method and finite element technique, approximate solutions are proposed and their convergence is analyzed.

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