Advances in Differential Equations

Non autonomous parabolic problems with unbounded coefficients in unbounded domains

L. Angiuli and L. Lorenzi

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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

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

First available in Project Euclid: 18 August 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

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