On minimal thinness, reduced functions and Green potentials

DOI10.1017/S0013091500005915zbMath0789.31001MaRDI QIDQ4289433

Matts Essén

Publication date: 3 May 1994

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Dirichlet problemsuperharmonic functionminimal thinnessWhitney decompositionfunctions of type \(W\)minimum principle of Beurling

Mathematics Subject Classification ID

Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15) Potentials and capacities, extremal length and related notions in higher dimensions (31B15) Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions (31A20)

Related Items

On boundary layers ⋮ Sets of Determination for Harmonic Functions ⋮ New criteria for minimal thinness and rarefiedness associated with cylindrical Schrödinger operator and their geometrical properties ⋮ On Lundh's percolation diffusion ⋮ Representation of continuous functions as sums of Green functions ⋮ Martin boundary of unlimited covering surfaces ⋮ Percolation diffusion. ⋮ Minimal Thinness and the Beurling Minimum Principle ⋮ Champagne subregions of the unit disc ⋮ Harmonic measure of the outer boundary of colander sets

Cites Work

• Sur le rôle de la frontière de R. S. Martin dans la théorie du potentiel
• ON BOUNDARY BEHAVIOUR OF BLASCHKE PRODUCTS
• Bases for Positive Continuous Functions
• Weak L 1 Characterizations of Poisson Integrals, Green Potentials, and H p Spaces
• A Minimum Principle for Positive Harmonic Functions
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