# The boundary Harnack principle for the fractional Laplacian

Studia Mathematica (1997)

- Volume: 123, Issue: 1, page 43-80
- ISSN: 0039-3223

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topBogdan, Krzysztof. "The boundary Harnack principle for the fractional Laplacian." Studia Mathematica 123.1 (1997): 43-80. <http://eudml.org/doc/216379>.

@article{Bogdan1997,

abstract = {We study nonnegative functions which are harmonic on a Lipschitz domain with respect to symmetric stable processes. We prove that if two such functions vanish continuously outside the domain near a part of its boundary, then their ratio is bounded near this part of the boundary.},

author = {Bogdan, Krzysztof},

journal = {Studia Mathematica},

keywords = {boundary Harnack principle; symmetric stable processes; harmonic functions; Lipschitz domains; Laplacian; fractional powers; symmetric stable semigroup; Riesz potentials},

language = {eng},

number = {1},

pages = {43-80},

title = {The boundary Harnack principle for the fractional Laplacian},

url = {http://eudml.org/doc/216379},

volume = {123},

year = {1997},

}

TY - JOUR

AU - Bogdan, Krzysztof

TI - The boundary Harnack principle for the fractional Laplacian

JO - Studia Mathematica

PY - 1997

VL - 123

IS - 1

SP - 43

EP - 80

AB - We study nonnegative functions which are harmonic on a Lipschitz domain with respect to symmetric stable processes. We prove that if two such functions vanish continuously outside the domain near a part of its boundary, then their ratio is bounded near this part of the boundary.

LA - eng

KW - boundary Harnack principle; symmetric stable processes; harmonic functions; Lipschitz domains; Laplacian; fractional powers; symmetric stable semigroup; Riesz potentials

UR - http://eudml.org/doc/216379

ER -

## References

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- [11] D. S. Jerison and C. E. Kenig, Boundary behavior of harmonic functions in non-tangentially accessible domains, Adv. in Math. 46 (1982), 80-147. Zbl0514.31003
- [12] D. S. Jerison and C. E. Kenig, Boundary value problems on Lipschitz domains, in: W. Littman (ed.), Studies in Partial Differential Equations, MAA Stud. Math. 23, Math. Assoc. Amer., 1982, 1-68. Zbl0529.31007
- [13] N. S. Landkof, Foundations of Modern Potential Theory, Springer, New York, 1972.
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