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In this paper, we prove that if every bounded $\mathcal A$-harmonic function on a complete Riemannian manifold $M$ is asymptotically constant at infinity of $p$-nonparabolic ends of $M$, then each bounded $\mathcal A$-harmonic function is uniquely determined by the values at infinity of $p$-nonparabolic ends of $M$, where $\mathcal A$ is a nonlinear elliptic operator of type $p$ on $M$. Furthermore, in this case, every bounded $\mathcal A$-harmonic function on $M$ has finite energy.
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참고문헌 (17)
참고문헌 신청
U. Abresch / 1990 / On complete manifolds with nonnegative Ricci curvature / J. Amer. Math. Soc. 3(2):355~374
J. Cheeger / 1972 / The splitting theorem for manifolds of nonnegative Ricci curvature / J. Differential Geometry 6:119~128
T. Coulhon / 1995 / Varietes riemanniennes isometriques a l'infini / Rev. Mat. Iberoamericana 11(3):687~726
J. Heinonen / 1993 / Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford Mathematical Monographs / The Clarendon Press;Oxford University Press
E. Hewitt / 1975 / Real and Abstract Analysis / Springer-Verlag
J. Cheeger / 1972 / The splitting theorem for manifolds of nonnegative Ricci curvature / J. Differential Geometry 6:119~128
T. Coulhon / 1995 / Varietes riemanniennes isometriques a l'infini / Rev. Mat. Iberoamericana 11(3):687~726
J. Heinonen / 1993 / Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford Mathematical Monographs / The Clarendon Press;Oxford University Press
E. Hewitt / 1975 / Real and Abstract Analysis / Springer-Verlag
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