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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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##### References:
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