Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-25T17:42:24.546Z Has data issue: false hasContentIssue false
  • English
  • Français

Liouville's Theorem in the Radially Symmetric Case

Published online by Cambridge University Press:  20 November 2018

Richard Froese
Richard Froese*
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, British Columbia, V6T 1Z4 e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We present a very short proof of Liouville's theorem for solutions to a non-uniformly elliptic radially symmetric equation. The proof uses the Ricatti equation satisfied by the Dirichlet to Neumann map.

Keywords

35B0534A30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 3 , 01 September 2005 , pp. 405 - 408
Copyright
Copyright © Canadian Mathematical Society 2005

References

[B] Barlow, M. T., On the Liouville property for divergence form operators. Canad. J. Math. 50(1998), 487–496.Google Scholar
[BCN] Berestycki, H., Caffarelli, L., and Nirenberg, L., Further qualitative properties for elliptic equations in unbounded domains. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25(1997), 69–94.Google Scholar
[GG] Ghoussoub, N. and Gui, C., On a conjecture of De Giorgi and some related problems. Math. Ann. 311(1998), 481–491.Google Scholar
[L] Losev, A. G., Some Liouville theorems on Riemannian manifolds of a special type. Izv. Vyssh. Uchebn. Zaved. Mat. (1991), 15–24; English Transl., Soviet Math. (Iz. VUZ) 35(1991), 15–23.Google Scholar
[LM] Losev, A. G. and Mazepa, E. A., Bounded solutions of the Schrödinger equation on Riemannian products. (Russian) Algebra i Analiz 13(2001), 84–110. translation in St. PetersburgMath. J. 13(2002), 57–73.Google Scholar