Schauder theory for Dirichlet elliptic operators in divergence form
Schauder theory for Dirichlet elliptic operators in divergence form
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DOI：
10.1007/s00028-013-0186-2
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发表时间：
2013-03
影响因子：
1.4
通讯作者：
Y. Miyazaki
中科院分区：
文献类型：
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作者：
Y. Miyazaki
设Abe是一个强椭圆算子，其指数的Hölder系数连续，且定义在Ω的一致C1 +σ区域上.当A是一个从m + σ阶Hölder空间到−m+ σ阶Hölder空间的算子时，我们证明了λ的逆（A− λ）− 1存在于复平面的一个适当的角域中，并估计了它的算子范数.作为应用，我们给出了椭圆型方程的一个正则性定理。
LetAbe a strongly elliptic operator of order 2min divergence form with Hölder continuous coefficients of exponentdefined in a uniformlyC1+σdomain Ω of. RegardingAas an operator from the Hölder space of orderm+ σ associated with the Dirichlet data to the Hölder space of order −m+ σ, we show that the inverse (A− λ)−1exists for λ 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.