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1.
In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic
shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region occupied by the
product (martensite) phase, which can occur in two variants (twins). The model, first proposed by Kohn and Müller (Philos
Mag A 66(5):697–715, 1992), is defined by the following functional:
(E)(u) = 2pb||u(0,·)||2[(H)\dot]1/2([0,h]) + ò0L dx ò0h dy ( |ux|2 + \frace2|uyy| ),\mathcal (E)(u) = 2\pi\beta||u(0,\cdot)||^2_{\dot H^{1/2}([0,h])} + \int_{0}^{L} dx \int_0^h dy\, \big( |u_x|^2 + \frac{\varepsilon}2|u_{yy}| \big), 相似文献
2.
This paper considers Hardy–Lieb–Thirring inequalities for higher order differential operators. A result for general fourth-order
operators on the half-line is developed, and the trace inequality
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