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ENERGY FINITE SOLUTIONS OF ELLIPTIC EQUATIONS ON RIEMANNIAN MANIFOLDS
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 Title & Authors
ENERGY FINITE SOLUTIONS OF ELLIPTIC EQUATIONS ON RIEMANNIAN MANIFOLDS
Kim, Seok-Woo; Lee, Yong-Hah;
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 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
1.
The connectivity at infinity of a manifold and Lq,p-Sobolev inequalities, Expositiones Mathematicae, 2014, 32, 4, 365  crossref(new windwow)
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