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) ds 2 0 ) to N (n β₯ 3), which was also called a quasiharmonic sphere (cf. Lin and Wang (1999) [1]). (Here ds 2 0 is the Euclidean metric in R n .) It arises from the blow-
β¦ LIBER β¦
A sharpLq-Liouville theorem forp-harmonic functions
β Scribed by Ilkka Holopainen
- Publisher
- The Hebrew University Magnes Press
- Year
- 2000
- Tongue
- English
- Weight
- 609 KB
- Volume
- 115
- Category
- Article
- ISSN
- 0021-2172
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We prove that any finitely connected domain in the plane can be distorted so that it becomes ''graviequivalent'' to a signed measure with arbitrarily small support. Precisely: if D ; β«ήβ¬ is a bounded, finitely connected domain with analytic Ε½ . boundary then for any a g D and r ) 0, ) 0 with B a, r