Let $f$ and $g$ be distinct real-valued harmonic functions, which not merely differ by a constant or are not merely multiples of each other. Also, assume that the first order partial derivatives of the two functions do not vanish identically. Is it true that in such a case the expression $f_xg_x+f_yg_y+f_zg_z$ will attain positive as well as negative values?
2026-04-01 07:56:16.1775030176
Value of $f_x g_x+ f_y g_y + f_z g_z$ when $f$ and $g$ are harmonic
32 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in HARMONIC-FUNCTIONS
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