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ASYMPTOTIC BEHAVIOR OF A-HARMONIC FUNCTIONS AND p-EXTREMAL LENGTH

이상문|이용하|김석우
대한수학회 (The Korean Mathematical Society)|2010.03|대한수학회보 (Bulletin of the KMS)|제47권 제2호|pp. 423-432

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참고문헌

키워드

maximum principlecomparison principlep-harmonic boundaryA-harmonic functionp-extremal lengthp-almost every curve
주제분류수학

초록

We describe the asymptotic behavior of functions of the Royden p-algebra in terms of p-extremal length. We also prove that each bounded A-harmonic function with finite energy on a complete Riemannian manifold is uniquely determined by the behavior of the function along p-almost every curve.

Abstract

We describe the asymptotic behavior of functions of the Royden p-algebra in terms of p-extremal length. We also prove that each bounded A-harmonic function with finite energy on a complete Riemannian manifold is uniquely determined by the behavior of the function along p-almost every curve.

참고문헌 (13)

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  8. S. Rickman, "Quasiregular Mappings. in: Ergebnisse Mathematik und ihrer Grenzgebiete" (1993), Springer-Verlag
  9. L. Sario, "Classification Theory of Riemann Surfaces" (1970), Springer Verlag
  10. H. Tanaka, "Harmonic boundaries of Riemannian manifolds", Nonlinear Anal., 14(1), pp.55~67 (1990)
  11. J. Väisälä, "Lectures on n-Dimensional Quasiconformal Mappings" (1971), Springer-Verlag
  12. W. P. Ziemer, "Extremal length and p-capacity", Michigan Math. J., 16, pp.43~51 (1969)
  13. W. P. Ziemer, "Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation" (1989), Springer-Verlag

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