Schauder theory for Dirichlet elliptic operators in divergence form

作者：Miyazaki Yoichi^*

来源：Journal of Evolution Equations, 2013, 13(2): 443-480.

DOI：10.1007/s00028-013-0186-2

• Elliptic operator in divergence form
• Dirichlet boundary condition
• Schauder estimate
• Holder space
• Regularity theorem

Let A be a strongly elliptic operator of order 2m in divergence form with Holder continuous coefficients of exponent defined in a uniformly C (1+sigma) domain Omega of . Regarding A as an operator from the Holder space of order m + sigma associated with the Dirichlet data to the Holder space of order -m + sigma, we show that the inverse (A - lambda)(-1) exists for lambda in a suitable angular region of the complex plane and estimate its operator norms. As an application, we give a regularity theorem for elliptic equations.

• 出版日期2013-6