ENERGY FINITE SOLUTIONS OF ELLIPTIC EQUATIONS ON RIEMANNIAN MANIFOLDS

- Journal title : Journal of the Korean Mathematical Society
- Volume 45, Issue 3, 2008, pp.807-819
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2008.45.3.807

Title & Authors

ENERGY FINITE SOLUTIONS OF ELLIPTIC EQUATIONS ON RIEMANNIAN MANIFOLDS

Kim, Seok-Woo; Lee, Yong-Hah;

Kim, Seok-Woo; Lee, Yong-Hah;

Abstract

We prove that for any continuous function f on the s-harmonic << 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 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 which vanish at the boundary ${\partial}E_{\iota}\;for\;{\iota}

Keywords

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

Language

English

Cited by

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