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2007 Second-order parabolic equations with unbounded coefficients in exterior domains
Matthias Hieber, Luca Lorenzi, Abdelaziz Rhandi
Differential Integral Equations 20(11): 1253-1284 (2007).

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

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Matthias Hieber. Luca Lorenzi. Abdelaziz Rhandi. "Second-order parabolic equations with unbounded coefficients in exterior domains." Differential Integral Equations 20 (11) 1253 - 1284, 2007.

Information

Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1212.35037
MathSciNet: MR2372426

Subjects:
Primary: 35K20
Secondary: 35B45 , 35B65 , 47D06

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.20 • No. 11 • 2007
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