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math.NA2025
Layer Potential Methods for Doubly-Periodic Harmonic Functions
Bohyun Kim, Braxton Osting
We develop and analyze layer potential methods to represent harmonic functions on finitely-connected tori (i.e., doubly-periodic harmonic functions). The layer potentials are expre…
math.NA2023
Harmonic functions on finitely-connected tori
Chiu-Yen Kao, Braxton Osting, Édouard Oudet
In this paper, we prove a Logarithmic Conjugation Theorem on finitely-connected tori. The theorem states that a harmonic function can be written as the real part of a function whos…