Singular Integrals and Elliptic Boundary Problems on Regular Semmes–Kenig–Toro Domains
Singular Integrals and Elliptic Boundary Problems on Regular Semmes–Kenig–Toro Domains
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正则 Semmes-Kenig-Toro 域上的奇异积分和椭圆边界问题
DOI：
10.1093/imrn/rnp214
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发表时间：
2009
影响因子：
1
通讯作者：
Michael Taylor
中科院分区：
文献类型：
--
作者：
S. Hofmann;M. Mitrea;Michael Taylor
我们发展了层势理论和相关的奇异积分算子，作为研究由Semmes[105,106]和Kenig和Toro[64-66]引入的一族域（我们称之为正则Semmes-Kenig-Toro域）上的各种椭圆边界问题的工具。这本书从几个方面扩展了Fabes、Jodeit和Riviere的经典作品。首先，一类域是函数的局部图，其梯度具有消失的平均振荡（vmo1域），它又包含一类c1域。此外，我们不仅研究了Dirichlet和Neumann边界问题，还研究了其他各种边界问题。此外，我们不仅处理常系数算子，还处理变系数算子，包括流形上的算子。
We develop the theory of layer potentials and related singular integral operators as a tool to study a variety of elliptic boundary problems on a family of domains introduced by Semmes [105, 106] and Kenig and Toro[64-66], which we call regular Semmes-Kenig-Toro domains. This extends the classic work of Fabes, Jodeit, and Riviere in several ways. For one, the class of domains that are locally graphs of functions whose gradients have vanishing mean oscillation (VMO 1 domains), which in turn contains the class of C 1 domains. In addition, we study not only the Dirichlet and Neumann boundary problems but also a variety of others. Furthermore, we treat not only constant coefficient operators but also operators with variable coefficients, including operators on manifolds.