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• W2071959134 abstract "Abstract Let N be a compact Riemannian manifold. A self-similar solution for the heat flow is a harmonic map from ( R n , e − | x | 2 / 2 ( n − 2 ) d s 0 2 ) to N ( n ≥ 3 ), which was also called a quasi-harmonic sphere (cf. Lin and Wang (1999) [1] ). (Here d s 0 2 is the Euclidean metric in R n .) It arises from the blow-up analysis of the heat flow at a singular point. When N = R and without the energy constraint, we call this a quasi-harmonic function. In this paper, we prove that there is neither a nonconstant positive quasi-harmonic function nor a nonconstant L p ( R n , e − | x | 2 / 2 ( n − 2 ) d s 0 2 ) ( p > n n − 2 ) quasi-harmonic function. However, for all 1 ≤ p ≤ n / ( n − 2 ) , there exists a nonconstant quasi-harmonic function in L p ( R n , e − | x | 2 / 2 ( n − 2 ) d s 0 2 ) ." @default.
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• W2071959134 date "2010-11-01" @default.
• W2071959134 modified "2023-09-29" @default.
• W2071959134 title "Liouville theorems for quasi-harmonic functions" @default.
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• W2071959134 doi "https://doi.org/10.1016/j.na.2010.06.045" @default.
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