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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.
