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Published in:
2001 | OriginalPaper | Chapter
Harmonic Functions
Authors : David H. Armitage, Stephen J. Gardiner
Published in: Classical Potential Theory
Publisher: Springer London
Included in: Professional Book Archive
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Our starting point is Laplace’s equation Δh= 0 on an open subset Ω of ℝ N, where % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaey % ypa0JaeyOaIy7aaWbaaSqabeaacaaIYaaaaOGaai4laiabgkGi2kaa % dIhadaqhaaWcbaGaaGymaaqaaiaaikdaaaGccqGHRaWkcqWIVlctcq % GHRaWkcqGHciITdaahaaWcbeqaaiaaikdaaaGccaGGVaGaeyOaIyRa % amiEamaaDaaaleaacaWGobaabaGaaGOmaaaakiaac6caaaa!4B16!$$\Delta = {\partial ^2}/\partial x_1^2 + \cdots + {\partial ^2}/\partial x_N^2.$$