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MiS Preprint
16/2003

Rigidity Estimate for Two Incompatible Wells

Nirmalendu Chaudhuri and Stefan Müller

Abstract

In this article we show that the $L^2$ distance of $\nabla u$ from a single matrix in $K$ is bounded by a multiple of $L^2$ distance from the set $K:=\,SO(n)\cup SO(n)\,H$, $H:={\rm diag}(\lambda_1,\cdots \lambda_n)$, $\lambda_i>0$ with ${\displaystyle \sum_{i=1}^{n}(1-\lambda_i)(1-{\rm det}H/\lambda_i)\,>\,0}$, which generalizes the rigidity estimate of Friesecke, James and M\"uller [9] for one well.

Received:
Feb 18, 2003
Published:
Feb 18, 2003

Related publications

inJournal
2004 Repository Open Access
Nirmalendu Chaudhuri and Stefan Müller

Rigidity estimate for two incompatible wells

In: Calculus of variations and partial differential equations, 19 (2004) 4, pp. 379-390