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November/December 2015 Non autonomous parabolic problems with unbounded coefficients in unbounded domains
L. Angiuli, L. Lorenzi
Adv. Differential Equations 20(11/12): 1067-1118 (November/December 2015).

Abstract

Given a class of nonautonomous elliptic operators $\mathcal A(t)$ with unbounded coefficients, defined in $\overline{I \times \Omega}$ (where $I$ is a right-halfline or $I=\mathbb R$ and $\Omega\subset \mathbb R^d$ is possibly unbounded), we prove existence and uniqueness of the evolution operator associated to $\mathcal A(t)$ in the space of bounded and continuous functions, under Dirichlet and first order, non tangential homogeneous boundary conditions. Some qualitative properties of the solutions, the compactness of the evolution operator and some uniform gradient estimates are then proved.

Citation

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L. Angiuli. L. Lorenzi. "Non autonomous parabolic problems with unbounded coefficients in unbounded domains." Adv. Differential Equations 20 (11/12) 1067 - 1118, November/December 2015.

Information

Published: November/December 2015
First available in Project Euclid: 18 August 2015

zbMATH: 1334.35073
MathSciNet: MR3388893

Subjects:
Primary: 35B65 , 35K10 , 35K15

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.20 • No. 11/12 • November/December 2015
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