Singular Perturbation as a Selection Criterion for Young‐Measure Solutions

Lilli, Markus; Healey, Timothy J.; Kielhöfer, Hansjörg

doi:10.1137/060656978

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Necessary Condition For Uniqueness Of the Global Minimizer1

Introduction1

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2007

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Cited by 2 publications

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“…By methods introduced in [19,20] one can show, that the same results holds if one considers a double-well potential W typical in non-linear elasticity, which means …”

Section: Necessary Condition For Uniqueness Of the Global Minimizersupporting

confidence: 57%

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Qualitative Behavior of Local Minimizers of Singular Perturbed Variational Problems

Lilli

2007

J Elasticity

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We consider a non-convex variational problem (P) and the corresponding singular perturbed problem (P ε ). The qualitative behavior of stable critical points of (P ε ) depending on ε and a lower order term is discussed and we prove compactness of a sequence of stable critical points as ε 0. Moreover we show whether this limit is the global minimizer of (P). Furthermore uniform convergence is considered as well as the convergence rate depending on ε.

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“…By methods introduced in [19,20] one can show, that the same results holds if one considers a double-well potential W typical in non-linear elasticity, which means …”

Section: Necessary Condition For Uniqueness Of the Global Minimizersupporting

confidence: 57%

“…[16,17]) as well as non-elliptic Euler-Lagrange equations (see e.g. [10,[13][14][15][18][19][20]), because singular perturbed problems are amenable to fairly standard existence methods for each ε > 0. But from our point of view, the advantage of introducing a higher gradient model is not just a theoretical one.…”

Section: Introductionmentioning

confidence: 99%