Journal
PACIFIC JOURNAL OF MATHEMATICS
Volume 250, Issue 2, Pages 319-334Publisher
PACIFIC JOURNAL MATHEMATICS
DOI: 10.2140/pjm.2011.250.319
Keywords
harmonic function; overdetermined elliptic problem; extremal domain; minimal surface
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Funding
- [ANR-08-BLANC-0335-01]
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A smooth flat Riemannian manifold is called an exceptional domain if it admits positive harmonic functions having vanishing Dirichlet boundary data and constant (nonzero) Neumann boundary data. In analogy with minimal surfaces, a representation formula is derived and applied to the classification of exceptional domains. Some interesting open problems are proposed along the way.
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