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초록· 키워드
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We prove that for any continuous function f on the s-harmonic
(1 < s < ∞) 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 E₁,E₂,...,El 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 Ei which vanish at the
boundary ∂Ei for i = 1, 2,..., l.
목차
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참고문헌 (13)
참고문헌 신청
A. A. Grigoryan / 1987 / On the set of positive solutions of the Laplace-Beltrami equation on Riemannian manifolds of a special form / Izvestiya Vysshikh Uchebnykh Zavedeniui
C. J. Sung / 2000 / Spaces of harmonic functions / Journal of the London Mathematical Society 61 (3) : 789 ~ 806
E. Hewitt / 1965 / Real and Abstract Analysis. A Modern Treatment of the Theory of Functions of a Real Variable / Springer-Verlag
H. Donnelly / 1986 / Bounded harmonic functions and positive Ricci curvature / Mathematische Zeitschrift 191 (4) : 559 ~ 565
I. Holopainen / 1994 / Solutions of elliptic equations on manifolds with roughly Euclidean ends / Mathematische Zeitschrift 217 (3) : 459 ~ 477
C. J. Sung / 2000 / Spaces of harmonic functions / Journal of the London Mathematical Society 61 (3) : 789 ~ 806
E. Hewitt / 1965 / Real and Abstract Analysis. A Modern Treatment of the Theory of Functions of a Real Variable / Springer-Verlag
H. Donnelly / 1986 / Bounded harmonic functions and positive Ricci curvature / Mathematische Zeitschrift 191 (4) : 559 ~ 565
I. Holopainen / 1994 / Solutions of elliptic equations on manifolds with roughly Euclidean ends / Mathematische Zeitschrift 217 (3) : 459 ~ 477
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