On the Boundary Behavior of Solutions to Elliptic and Parabolic Equations—with Applications to Boundary Control for Parabolic Equations
On the Boundary Behavior of Solutions to Elliptic and Parabolic Equations—with Applications to Boundary Control for Parabolic Equations
复制标题
DOI：
10.1137/0316040
复制
发表时间：
1978-07
影响因子：
2.2
通讯作者：
E. Schmidt;N. Weck
中科院分区：
文献类型：
--
作者：
E. Schmidt;N. Weck
结果表明，对于具有无限可微边界的有界域，二阶椭圆方程（涉及无限可微系数）和相关抛物线方程的解不能与其在具有正测度的边界子集上的法态导数一起消失。这一事实对于抛物方程的边界控制问题有多种应用。先前获得的结果需要对边界和系数进行分析性假设。
It is shown that for bounded domains with infinitely differentiable boundaries solutions of second order elliptic equations (involving infinitely differentiable coefficients), and of the associated parabolic equations, cannot vanish together with their normal derivatives on subsets of the boundary having positive measure. This fact has multiple applications to the boundary control problem for parabolic equations. The results obtained have previously required an analyticity assumption on the boundary and on the coefficients.