Abstract
Let D be a nonempty open subset of ℝN. If N > 2 or if N = 2 and D is bounded, the function G(ξ, •) is lower bounded for each point ξ of D; so GM D G(ξ, •) exists (Section III. 1). If N = 2, if D is unbounded, and if G(ξ, •) has a subharmonic minorant on D for some ξ in D, then the minorant GM D G(ξ, •) exists for every ξ in D.
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© 1984 Springer-Verlag New York Inc.
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Doob, J.L. (1984). Green Functions. In: Classical Potential Theory and Its Probabilistic Counterpart. Grundlehren der mathematischen Wissenschaften, vol 262. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5208-5_7
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DOI: https://doi.org/10.1007/978-1-4612-5208-5_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-9738-3
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