Existence and regularity for scalar minimizers of affine nonconvex simple integrals.
type: Item
instance of: scholarly article
title: Existence and regularity for scalar minimizers of affine nonconvex simple integrals.
zbMATH Open document ID: 1039.49032
DOI: 10.1016/S0362-546X(02)00309-7
author: António Ornelas
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-04-27T00:00:00Z
review text: The author studies the existence of minimizers for functionals of the form \(\int_a^b \{ \rho(x)h(x') + \varphi(x)\}dt\), where \(\rho~:~{\mathbf R}\mapsto [1,\infty)\), \(h~:~{\mathbf R}\mapsto [1,\infty]\), \(\varphi~:~{\mathbf R}\mapsto {\mathbf R} \). It is supposed that \(\varphi\) is lower semicontinuous and bounded from below, and that \(h\) is not necessarily convex, but it satisfies the condition \(h^{**}(0)=h(0)\). It is proved that the above functional admits absolutely continuous minimizers satisfying prescribed values at \(a\) and \(b\). Under some additional conditions the author proves that the minimizers are Lipschitz continuous.
reviewed by: J-P Raymond
Mathematics Subject Classification ID: 49N60
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 49J05
zbMATH DE Number: 1900942
zbMATH Keywords: calculus of variations
zbMATH Keywords: nonconvex integrands
zbMATH Keywords: existence
zbMATH Keywords: regularity
MaRDI profile type: Publication
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full work available at URL: s0362-546x(02)00309-7
OpenAlex ID: W2012908026
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description: scientific article; zbMATH DE number 1900942