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When u=u(x)>0 is a smooth non-constant function in R^n and is sub-harmonic in R^n, i.e. Laplacian u \geq 0 in R^n, can we conclude that u is unbounded in R^n? -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.112.4.207
JASS0213 :應該是對的,對所有0球心的n-1為球殼上取最大值 03/19 01:35
JASS0213 :Max principle告訴我們這個關於半徑r的函數是非遞減 03/19 01:36
JASS0213 :我現在想到的作法似乎有點囉嗦。 03/19 01:47
JASS0213 :google 一下 Liouville's theorem吧 03/19 02:11