Poisson kernel characterization of Reifenberg flat chord arc domains

Carlos E. Kenig; Tatiana Toro

Annales scientifiques de l'École Normale Supérieure (2003)

  • Volume: 36, Issue: 3, page 323-401
  • ISSN: 0012-9593

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Kenig, Carlos E., and Toro, Tatiana. "Poisson kernel characterization of Reifenberg flat chord arc domains." Annales scientifiques de l'École Normale Supérieure 36.3 (2003): 323-401. <http://eudml.org/doc/82604>.

@article{Kenig2003,
author = {Kenig, Carlos E., Toro, Tatiana},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Poisson kernel; harmonic measure; free boundary; regularity; mean oscillation},
language = {eng},
number = {3},
pages = {323-401},
publisher = {Elsevier},
title = {Poisson kernel characterization of Reifenberg flat chord arc domains},
url = {http://eudml.org/doc/82604},
volume = {36},
year = {2003},
}

TY - JOUR
AU - Kenig, Carlos E.
AU - Toro, Tatiana
TI - Poisson kernel characterization of Reifenberg flat chord arc domains
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2003
PB - Elsevier
VL - 36
IS - 3
SP - 323
EP - 401
LA - eng
KW - Poisson kernel; harmonic measure; free boundary; regularity; mean oscillation
UR - http://eudml.org/doc/82604
ER -

References

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  1. [1] Alt H.W., Caffarelli L.A., Existence and regularity for a minimum problem with free boundary, J. Reine Angew. Math.325 (1981) 105-144. Zbl0449.35105MR618549
  2. [2] David G., Wavelets and Singular Integrals on Curves and Surfaces, Lecture Notes in Math., 1465, Springer-Verlag, 1991. Zbl0764.42019MR1123480
  3. [3] do Carmo M., Riemannian Geometry, Birkhäuser, 1992. Zbl0752.53001MR1138207
  4. [4] David G., Jerison D., Lipschitz approximation to hypersurfaces, harmonic measure, and singular integrals, Indiana Univ. Math. J.39 (1990) 831-845. Zbl0758.42008MR1078740
  5. [5] David G., Semmes S., Analysis of and on Uniformly Rectifiable Sets, Mathematical Surveys and Monographs, AMS Series, 1993. Zbl0832.42008MR1251061
  6. [6] Duren P., The Theory of Hp Spaces, Academic Press, New York, 1970. Zbl0215.20203MR268655
  7. [7] Evans L.C., Gariepy R.F., Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, CRC Press, 1992. Zbl0804.28001MR1158660
  8. [8] Federer H., Geometric Measure Theory, Springer-Verlag, 1969. Zbl0874.49001MR257325
  9. [9] García-Cuerva J., Rubio de Francia J.L, Weighted Norm Inequalities and Related Topics, Math. Studies, 116, North Holland, Amsterdam, 1985. Zbl0578.46046MR848147
  10. [10] Garnett J.B., Jones P.W., The distance in BMO to L, Ann. of Math.108 (1978) 373-393. Zbl0383.26010MR506992
  11. [11] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1983. Zbl0562.35001MR737190
  12. [12] Helms L.L., Introduction to Potential Theory, Pure and Applied Mathematics, 22, 1975. Zbl0188.17203MR460666
  13. [13] Jerison D., Regularity of the Poisson kernel and free boundary problems, Colloquium Math.60–61 (1990) 547-567. Zbl0732.35025MR1096396
  14. [14] Jerison D., Kenig C., Boundary behavior of harmonic functions in nontangentially accessible domains, Adv. Math.46 (1982) 80-147. Zbl0514.31003MR676988
  15. [15] Jerison D., Kenig C., The logarithm of the Poisson kernel of a C1 domain has vanishing mean oscillation, Trans. Amer. Math. Soc.273 (1982) 781-794. Zbl0494.31003MR667174
  16. [16] John F., Nirenberg L., On functions of bounded mean oscillation, Comm. Pure Appl. Math.14 (1961) 415-426. Zbl0102.04302MR131498
  17. [17] Keldysh M.V., Lavrentiev M.A., Sur la représentation conforme des domaines limités par des courbes rectifiables, Ann. Scient. Éc. Norm. Sup.54 (1937) 1-38. Zbl0017.21702
  18. [18] Kenig C., Toro T., Free boundary regularity for harmonic measures and Poisson kernels, Ann. of Math.150 (1999) 369-454. Zbl0946.31001MR1726699
  19. [19] Kenig C., Toro T., Harmonic measure on locally flat domains, Duke Math. J.87 (1997) 509-551. Zbl0878.31002MR1446617
  20. [20] Kenig C., Toro T., On the free boundary regularity theorem of Alt and Caffarelli, Discrete and Continuous Dynamical Systems (in press). Zbl1051.31001
  21. [21] Morrey C.B., Multiple Integrals in the Calculus of Variations, Springer-Verlag, 1966. Zbl0142.38701MR202511
  22. [22] Pommerenke Ch., On univalent functions, Bloch functions and VMOA, Math. Ann.236 (1978) 199-208. Zbl0385.30013MR492206
  23. [23] Reifenberg E., Solution of the Plateau problem for m-dimensional surfaces of varying topological type, Acta Math.104 (1960) 1-92. Zbl0099.08503MR114145
  24. [24] Semmes S., Chord-arc surfaces with small constant, II: Good parametrizations, Adv. Math.88 (1991) 170-199. Zbl0733.42016MR1120612
  25. [25] Semmes S., Analysis vs. geometry on a class of rectifiable hypersurfaces, Indiana Univ. J.39 (1990) 1005-1035. Zbl0796.42014MR1087183
  26. [26] Simon L., Lectures on Geometric Measure Theory, Australian National University, 1983. Zbl0546.49019MR756417

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