Advances in Differential Equations

Non autonomous parabolic problems with unbounded coefficients in unbounded domains

L. Angiuli and L. Lorenzi

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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.

Article information

Source
Adv. Differential Equations Volume 20, Number 11/12 (2015), 1067-1118.

Dates
First available in Project Euclid: 18 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.ade/1439901071

Mathematical Reviews number (MathSciNet)
MR3388893

Zentralblatt MATH identifier
1334.35073

Subjects
Primary: 35K10: Second-order parabolic equations 35K15: Initial value problems for second-order parabolic equations 35B65: Smoothness and regularity of solutions

Citation

Angiuli, L.; Lorenzi, L. Non autonomous parabolic problems with unbounded coefficients in unbounded domains. Adv. Differential Equations 20 (2015), no. 11/12, 1067--1118. https://projecteuclid.org/euclid.ade/1439901071.


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