论文标题
纳米板的强大独特延续和全球规律性估算
Strong unique continuation and global regularity estimates for nanoplates
论文作者
论文摘要
在本文中，我们分析了在弯曲变形中纳米板的应变梯度线性弹性理论框架中产生的第六阶椭圆算子的某些特性。首先，我们严格推断出基本的诺伊曼问题及其良好的姿势的薄弱表述。在某些适当的平滑度上，我们对诺伊曼问题解决方案的内部和边界规律性估计得出了一些合适的假设。最后，对于各向同性材料的情况，我们通过卡勒曼估计方法以加倍不平等和三个球体不等式的形式获得了内部新的强大独特延续结果。
In this paper we analyze some properties of a sixth order elliptic operator arising in the framework of the strain gradient linear elasticity theory for nanoplates in flexural deformation. We first rigorously deduce the weak formulation of the underlying Neumann problem as well as its well posedness. Under some suitable smoothness assumptions on the coefficients and on the geometry we derive interior and boundary regularity estimates for the solution of the Neumann problem. Finally, for the case of isotropic materials, we obtain new Strong Unique Continuation results in the interior, in the form of doubling inequality and three spheres inequality, by a Carlemann estimates approach.
