Abstract
Letu be an entire lower semicontinuous subsolution to the quasilinear elliptic equation divA(x,∇u)=0 in ℝn. It is shown that ifu is not bounded above, then there exists a path going to infinity along whichu tends to infinity. The result extends works of Talpur, Fuglede, and others. Growth aspects of subsolutions are also studied.
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Heinonen, J. Asymptotic paths for subsolutions of quasilinear elliptic equations. Manuscripta Math 62, 449–465 (1988). https://doi.org/10.1007/BF01357721
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DOI: https://doi.org/10.1007/BF01357721