论文标题
在尖锐的Agmon-Miranda最大原则上
On sharp Agmon-Miranda maximum principles
论文作者
论文摘要
在这项调查中，我们根据线性椭圆方程和系统的不同形式的最大原理制定结果。我们从经典最大模量原理的有效性的必要条件开始，用于二阶强烈椭圆形系统的解决方案。例如，该原理对系统系数的严格限制，例如，它因Stokes和Lamé系统而失败。接下来，由于S. Agmon和C. Miranda，我们以更一般的最大原则转向尖锐的常数。我们考虑了半个空间的高阶椭圆方程，stokes和Lamé系统，以及平面形成半平面状态的系统。
In this survey we formulate our results on different forms of maximum principles for linear elliptic equations and systems. We start with necessary and sufficient conditions for validity of the classical maximum modulus principle for solutions of second order strongly elliptic systems. This principle holds under rather heavy restrictions on the coefficients of the systems, for instance, it fails for the Stokes and Lamé systems. Next, we turn to sharp constants in more general maximum principles due to S. Agmon and C. Miranda. We consider higher order elliptic equations, Stokes and Lamé systems in a half-space as well as the system of planar deformed state in a half-plane.
