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Numerical analysis of oscillations in nonconvex problems. (English) Zbl 0712.65063
Let \(\phi\) : \({\mathbb{R}}^ n\to {\mathbb{R}}\) be a nonnegative function such that \(\phi (w_ 1)=\phi (w_ 2)=...=\phi (w_ k)=0.\) If \(a\in C\circ (w_ i)\), where \(C\circ (w_ i)\) denotes the convex hull of the \(w_ i's\), we consider the problem (*) \(\inf_{V_ a}\int_{\Omega}\phi (\nabla v(x))dx\), where \(V_ a\) denotes a space of functions such that \(v(x)=ax\) on \(\partial \Omega\). In the case where the infimum (*) is not achieved we study the pattern of the minimizing sequences estimating in terms of the mesh size the probability of a minimizing sequence to use the well \(w_ i\) in order to decrease the energy.
Reviewer: M.Chipot

MSC:
65K10 Numerical optimization and variational techniques
49J20 Existence theories for optimal control problems involving partial differential equations
49J40 Variational inequalities
49M15 Newton-type methods
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