Abstract
Let A be a strongly elliptic operator of order 2m in divergence form with Hölder continuous coefficients of exponent \({\sigma \in (0,1)}\) defined in a uniformly C 1+σ domain Ω of \({\mathbb{R}^n}\) . Regarding A as an operator from the Hölder space of order m + σ associated with the Dirichlet data to the Hölder space of order −m + σ, we show that the inverse (A − λ)−1 exists 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.
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Miyazaki, Y. Schauder theory for Dirichlet elliptic operators in divergence form. J. Evol. Equ. 13, 443–480 (2013). https://doi.org/10.1007/s00028-013-0186-2
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DOI: https://doi.org/10.1007/s00028-013-0186-2