A Riemann–Hilbert Approach to the Laplace Equation

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چکیده

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The Laplace Equation

Definition 1. Among the most important and ubiquitous of all partial differential equations is Laplace’s Equation: ∆u = 0, where the Laplacian operator ∆ acts on the function u : U → R (U is open in R) by taking the sum of the unmixed partial derivatives. For example: n = 1: ∆u = ∂ 2u ∂x2 = u = 0 In this simple case, the solution u = ax + b is found by integrating twice. n = 2: ∆u = ∂ 2u ∂x1 + ...

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ژورنال

عنوان ژورنال: Journal of Mathematical Analysis and Applications

سال: 2000

ISSN: 0022-247X

DOI: 10.1006/jmaa.2000.7052