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A Probabilistic Proof of the Boundary Harnack Principle

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Seminar on Stochastic Processes, 1989

Part of the book series: Progress in Probability ((PRPR,volume 18))

Abstract

The boundary Harnack principle may be stated as follows (cf. Jerison and Kenig (1982a), Theorem 5.25).

Research partially supported by NSF grants DMS 8701073 and DMS 8901255.

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References

  1. M.T. Barlow and R.F. Bass, The construction of Brownian motion on the Sierpiński carpet, Ann. de l’I. H. Poincaré (1989). (to appear)

    Google Scholar 

  2. R.F. Bass and K. Burdzy, The boundary Harnack principle for Hölder domains. (in preparation)

    Google Scholar 

  3. L. Caffarelli, E. Fabes, S. Mortola and S. Salsa, Boundary behavior of non-negative solutions of elliptic operarors in divergence form, Indiana Univ. Math. J. 30 (1981), 621–640.

    Article  MathSciNet  MATH  Google Scholar 

  4. B. Dahlberg, Estimates of harmonic measure, Arch. Rat. Mech. Anal. 65 (1977), 275–288.

    Article  MathSciNet  MATH  Google Scholar 

  5. J.L. Doob, “Classical Potential Theory and Its Probabilistic Counterpart,” Springer, New York, 1984.

    Book  MATH  Google Scholar 

  6. R. Durrett, “Brownian Motion and Martingales in Analysis,” Wadsworth, Belmont CA, 1984.

    MATH  Google Scholar 

  7. E. Fabes, N. Garofalo, S. Marin-Malave, and S. Salsa, Fatou theorems for some nonlinear elliptic equations. (preprint)

    Google Scholar 

  8. E. Fabes, N. Garofalo and S. Salsa, A backward Harnack inequality and Fatou theorem for non-negative solutions of parabolic equations, Illinois J. Math. 30 (1986), 536–565.

    MathSciNet  MATH  Google Scholar 

  9. R.R. Hunt and R.L. Wheeden, Positive harmonic functions on Lips-chitz domains, Trans. Amer. Math. Soc. 147 (1970), 507–527.

    Article  MathSciNet  MATH  Google Scholar 

  10. D.S. Jerison and C.E. Kenig, Boundary value problems on Lipschitz domains, in: Studies in Partial Differential Equations, ed. W. Littman, Washington, D.C.: Math. Assoc. Amer. (1982a).

    Google Scholar 

  11. D.S. Jerison and C.E. Kenig, Boundary behavior of harmonic functions in non-tangentially accessible domains, Adv. in Math. 46 (1982b), 80–147.

    Article  MathSciNet  MATH  Google Scholar 

  12. J.-M.G. Wu, Comparisons of kernel functions, boundary Harnack principle and relative Fatou theorem on Lipschitz domains, Ann. Inst. Fourier Grenoble 28 (1978), 147–167.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    Richard F. Bass & Krzysztof Burdzy

Authors
  1. Richard F. Bass
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  2. Krzysztof Burdzy
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Editor information

Editors and Affiliations

  1. Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ, 08544, USA

    E. Çinlar

  2. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    K. L. Chung

  3. Department of Mathematics, University of California, San Diego, La Jolla, CA, 92093, USA

    R. K. Getoor , P. J. Fitzsimmons  & R. J. Williams ,  & 

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© 1990 Birkhäuser Boston

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Bass, R.F., Burdzy, K. (1990). A Probabilistic Proof of the Boundary Harnack Principle. In: Çinlar, E., Chung, K.L., Getoor, R.K., Fitzsimmons, P.J., Williams, R.J. (eds) Seminar on Stochastic Processes, 1989. Progress in Probability, vol 18. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3458-6_1

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  • DOI: https://doi.org/10.1007/978-1-4612-3458-6_1

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-3457-5

  • Online ISBN: 978-1-4612-3458-6

  • eBook Packages: Springer Book Archive

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