Eigenfunctions and Harmonic Functions in Convex and Concave Domains

David Jerison
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David Jerison: Massachusetts Institute of Technology, Department of Mathematics

A chapter in Proceedings of the International Congress of Mathematicians, 1995, pp 1108-1117 from Springer

Abstract: Abstract Let Ω be a bounded, convex, open subset of R N . This paper concerns the behavior of positive harmonic functions that vanish on ∂Ω. We will consider both the case in which the function is defined in Ω and the case in which the function is defined in the complement of Ω. We will also discuss eigenfunctions defined in Ω. The theme is to study how the shape of Ω influences the size of solutions to these basic elliptic equations.

Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-9078-6_103

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DOI: 10.1007/978-3-0348-9078-6_103

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