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(2006)
Stagnation zones of harmonic function on surfaces and pre-Liuoville theorems
- Publisher
- de Gruyter
- Copyright
- © Heldermann Verlag
- ISSN
- 1072-947X
- eISSN
- 1072-9176
- DOI
- 10.1515/GMJ.2007.519
- Publisher site
- See Article on Publisher Site
Abstract
We investigate stagnation zones of solutions of partial differential elliptic equations. With the domain width being much less than its length and special boundary conditions, these solutions can be almost constant over large subdomains. Such domains are called stagnation zones (𝑠-zones). We estimate the size, the location of these 𝑠-zones and study the behavior of solutions on 𝑠-zones.
Journal
Georgian Mathematical Journal – de Gruyter
Published: Sep 1, 2007
Keywords: Stagnation zone; 𝐴-harmonic function; Laplace–Beltrami equation; capacity