Advances in Differential Equations

Classifying smooth supersolutions for a general class of elliptic boundary value problems

Julián López-Gómez

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This paper characterizes the pointwise behavior of smooth supersolutions of a general class of elliptic linear boundary value problems of mixed type. Our main result is a substantial extension of W.~Walter [9, Theorem 2] to cover the case of general mixed boundary conditions. As an application of this result, the theory of [6] is adapted to obtain a weak version---within the context of Schauder's theory---of the characterization of the strong maximum principle of H. Amann and J. López-Gómez [3].

Article information

Adv. Differential Equations, Volume 8, Number 9 (2003), 1025-1042.

First available in Project Euclid: 19 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J25: Boundary value problems for second-order elliptic equations
Secondary: 35B50: Maximum principles 35J15: Second-order elliptic equations


López-Gómez, Julián. Classifying smooth supersolutions for a general class of elliptic boundary value problems. Adv. Differential Equations 8 (2003), no. 9, 1025--1042.

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