[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2008.45.3.807

ENERGY FINITE SOLUTIONS OF ELLIPTIC EQUATIONS ON RIEMANNIAN MANIFOLDS

Kim, Seok-Woo (Department of Mathematics Education Konkuk University)
Lee, Yong-Hah (Department of Mathematics Education Ewha Womans University)

Publication Information

Journal of the Korean Mathematical Society / v.45, no.3, 2008 , pp. 807-819 More about this Journal

Abstract

We prove that for any continuous function f on the s-harmonic (1 boundary of a complete Riemannian manifold M, there exists a solution, which is a limit of a sequence of bounded energy finite solutions in the sense of supremum norm, for a certain elliptic operator A on M whose boundary value at each s-harmonic boundary point coincides with that of f. If $E_1,\;E_2,...,E_{\iota}$ are s-nonparabolic ends of M, then we also prove that there is a one to one correspondence between the set of bounded energy finite solutions for A on M and the Cartesian product of the sets of bounded energy finite solutions for A on $E_i$ which vanish at the boundary ${\partial}E_{\iota}\;for\;{\iota}=1,2,...,{\iota}$

Keywords

s-harmonic boundary; A-harmonic function; end;

Citations & Related Records

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