Gauss' theorem
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...This is called the mean value property. Conversely, under the assumption of continuity, a function that has this property is a harmonic function (Gauss' theorem). If u is harmonic in D , then u has no maximum or minimum value in D unless u is a constant. ... *Some of the terminology explanations that mention "Gauss' theorem" are listed below. Source | Heibonsha World Encyclopedia 2nd Edition | Information |
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…これを平均値性質という。逆に，連続性の仮定の下に，この性質をもつ関数は調和関数である(ガウスの定理Gauss’ theorem)。 uがDで調和のとき，uが定数でないかぎり，uはDにおいて最大値も最小値もとらない。… ※「Gauss' theorem」について言及している用語解説の一部を掲載しています。 出典｜株式会社平凡社世界大百科事典 第２版について | 情報 |
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