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non-conforming approximations

ESAIM: Control, Optimisation and Calculus of Variations (1)

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External approximation of first order variationalproblemsvia W-1,p estimates
Cesare Davini, Roberto Paroni
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 14 / Issue 4 / October 2008

Published online by Cambridge University Press:

30 January 2008, pp. 802-824

Print publication:

October 2008
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Here we present an approximation method for a rather broad class of first ordervariational problems in spaces of piece-wise constant functions overtriangulations of the base domain. The convergence of the method is based on aninequality involving $W^{-1, p}$ norms obtained by Nečas and on the generalframework of Γ-convergence theory.