On the existence of weighted boundary limits of harmonic functions

Yoshihiro Mizuta

Annales de l'institut Fourier (1990)

  • Volume: 40, Issue: 4, page 811-833
  • ISSN: 0373-0956

Abstract

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We study the existence of tangential boundary limits for harmonic functions in a Lipschitz domain, which belong to Orlicz-Sobolev classes. The exceptional sets appearing in this discussion are evaluated by use of Bessel-type capacities as well as Hausdorff measures.

How to cite

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Mizuta, Yoshihiro. "On the existence of weighted boundary limits of harmonic functions." Annales de l'institut Fourier 40.4 (1990): 811-833. <http://eudml.org/doc/74900>.

@article{Mizuta1990,
abstract = {We study the existence of tangential boundary limits for harmonic functions in a Lipschitz domain, which belong to Orlicz-Sobolev classes. The exceptional sets appearing in this discussion are evaluated by use of Bessel-type capacities as well as Hausdorff measures.},
author = {Mizuta, Yoshihiro},
journal = {Annales de l'institut Fourier},
keywords = {Bessel capacity; tangential boundary limits; Lipschitz domain},
language = {eng},
number = {4},
pages = {811-833},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the existence of weighted boundary limits of harmonic functions},
url = {http://eudml.org/doc/74900},
volume = {40},
year = {1990},
}

TY - JOUR
AU - Mizuta, Yoshihiro
TI - On the existence of weighted boundary limits of harmonic functions
JO - Annales de l'institut Fourier
PY - 1990
PB - Association des Annales de l'Institut Fourier
VL - 40
IS - 4
SP - 811
EP - 833
AB - We study the existence of tangential boundary limits for harmonic functions in a Lipschitz domain, which belong to Orlicz-Sobolev classes. The exceptional sets appearing in this discussion are evaluated by use of Bessel-type capacities as well as Hausdorff measures.
LA - eng
KW - Bessel capacity; tangential boundary limits; Lipschitz domain
UR - http://eudml.org/doc/74900
ER -

References

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  1. [1] M. BRELOT, Élément de la théorie classique du potentiel, 4e édition, Centre de Documentation Universitaire, Paris, 1969. 
  2. [2] L. CARLESON, Selected problems on exceptional sets, Van Nostrand, Princeton, 1967. Zbl0189.10903MR37 #1576
  3. [3] A. B. CRUZEIRO, Convergence au bord pour les fonctions harmoniques dans Rd de la classe de Sobolev Wd1, C.R.A.S., Paris, 294 (1982), 71-74. Zbl0495.31003MR83g:31006
  4. [4] N. G. MEYERS, A theory of capacities for potentials in Lebesgue classes, Math. Scand., 26 (1970), 255-292. Zbl0242.31006MR43 #3474
  5. [5] Y. MIZUTA, On the Boundary limits of harmonic functions with gradient in Lp, Ann. Inst. Fourier, 34-1 (1984), 99-109. Zbl0522.31009MR85f:31009
  6. [6] Y. MIZUTA, On the boundary limits of harmonic functions, Hiroshima Math. J., 18 (1988), 207-217. Zbl0664.31007MR89d:31015
  7. [7] T. MURAI, On the behavior of functions with finite weighted Dirichlet integral near the boundary, Nagoya Math. J., 53 (1974), 83-101. Zbl0293.31012MR50 #626
  8. [8] A. NAGEL, W. RUDIN and J. H. SHAPIRO, Tangential boundary behavior of functions in Dirichlet-type spaces, Ann. of Math., 116 (1982), 331-360. Zbl0531.31007MR84a:31002
  9. [9] E. M. STEIN, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, 1970. Zbl0207.13501MR44 #7280
  10. [10] H. WALLIN, on the existence of boundary values of a class of Beppo Levi functions, Trans. Amer. Math. Soc., 120 (1985), 510-525. Zbl0139.06301MR32 #5911

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