Abstract
In this paper, we consider elliptic and parabolic equations with unbounded coefficients in smooth exterior domains $\Omega\subset {\mathbb R}^N$, subject to Dirichlet or Neumann boundary conditions. Under suitable assumptions on the growth of the coefficients, the solution of the parabolic problem is governed by a semigroup $\{T(t)\}$ on $L^p(\Omega)$ for $1 < p < \infty$ and on $C_b(\overline\Omega)$. Furthermore, uniform- and $L^p$-estimates for higher-order spatial derivatives of $\{T(t)\}$ are obtained. They imply optimal Schauder estimates for the solution of the corresponding elliptic and parabolic problems.
Citation
Matthias Hieber. Luca Lorenzi. Abdelaziz Rhandi. "Second-order parabolic equations with unbounded coefficients in exterior domains." Differential Integral Equations 20 (11) 1253 - 1284, 2007. https://doi.org/10.57262/die/1356039288
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