Existence, uniqueness, and regularity in boundary problems for mixed order elliptic systems
Existence, uniqueness, and regularity in boundary problems for mixed order elliptic systems
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混合阶椭圆系统边界问题的存在性、唯一性和规律性
DOI：
10.1016/0022-0396(83)90056-6
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发表时间：
1983
期刊：
影响因子：
--
通讯作者：
J. A. Ladwig
中科院分区：
文献类型：
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作者：
J. A. Ladwig
Agmon，Douglis和Nirenberg在[1，II]中定义了混合阶偏微分方程组边值问题的椭圆性，并得到了相关的先验估计.本文将Freeman和Schechter在文[4]中对单个椭圆型方程边值问题建立的两个定理推广到ADN-椭圆型方程组，这两个定理在很大程度上依赖于文[41]的方法。第一个定理是半空间上解的存在性、唯一性和正则性的充分必要条件。也得到了一个有界的逆估计。与[4]一样，这里的证明是基于傅立叶变换方法，但我们在处理常微分方程的相关问题时与[4]不同。我们注意到，这里使用的方法还证明了先验估计与Agmon、Douglis和Nirenberg [11]的基本解方法不同。
Agmon, Douglis and Nirenberg in [1, II] defined ellipticity in the boundary problem for a system of mixed order partial differential equations and obtained the associated a priori estimates. In this paper we extend to ADN-elliptic systems two theorems established by Freeman and Schechter in [4] for boundary problems for a single elliptic equation, relying, for the most part, on the methods of (41.The first theorem is a condition, which is both necessary and sufficient, for the existence, uniqueness and regularity of solutions on a half-space. A bounded inverse estimate is also obtained. The proof here, as in [4], is based on a Fourier transform approach but we differ from [4] in our treatment of the associated problem for ordinary differential equations. We remark that the methods used here also yield a proof of the a priori estimate differing from the fundamental solution approach of Agmon, Douglis and Nirenberg [11.