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Separately harmonic and subharmonic functions

Abstract

Let u(x, y) be defined in B 1×B 2 where B 1⫅ℝm and B 2⫅ℝn, and assume that u(x, ·) harmonic for every fixed x and u(·, y) is subharmonic for every fixed y. We show that if u(·, y) is, in addition, C 2 for each y then u is subharmonic in B 1×B 2 in both variables jointly.

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Kołodziej, S., Thorbiörnson, J. Separately harmonic and subharmonic functions. Potential Anal 5, 463–466 (1996). https://doi.org/10.1007/BF00275514

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Mathematics Subject Classification (1991)

  • 31B05

Key words

  • Separately subharmonic functions