On the capillarity problem with constant volume
Claus Gerhardt (1975)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Claus Gerhardt (1975)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Michele Carriero, Antonio Leaci, Franco Tomarelli (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Italo Tamanini, Giuseppe Congedo (1991)
Rendiconti del Seminario Matematico della Università di Padova
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Eric Bonnetier, Richard S. Falk, Michael A. Grinfeld (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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The equilibrium configurations of a one-dimensional variational model that combines terms expressing the bulk energy of a deformable crystal and its surface energy are studied. After elimination of the displacement, the problem reduces to the minimization of a nonconvex and nonlocal functional of a single function, the thickness. Depending on a parameter which strengthens one of the terms comprising the energy at the expense of the other, it is shown that this functional may have a...
Danilo Percivale (1992)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Marc Oliver Rieger (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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Existence results for a class of one-dimensional abstract variational problems with volume constraints are established. The main assumptions on their energy are additivity, translation invariance and solvability of a transition problem. These general results yield existence results for nonconvex problems. A counterexample shows that a naive extension to higher dimensional situations in general fails.