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Volumn 123, Issue 1, 1997, Pages 43-80

The boundary Harnack principle for the fractional Laplacian

Author keywords

Boundary Harnack principle; Harmonic functions; Lipschitz domains; Symmetric stable processes

Indexed keywords


EID: 0031444990     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: 10.4064/sm-123-1-43-80     Document Type: Article
Times cited : (201)

References (17)
  • 2
    • 0002149688 scopus 로고
    • A probabilistic proof of the boundary Harnack principle
    • E. Çinlar, K. L. Chung, and R. K. Getoor (eds.), 1989, Birkhäuser, Boston
    • R. F. Bass and K. Burdzy, A probabilistic proof of the boundary Harnack principle, in: E. Çinlar, K. L. Chung, and R. K. Getoor (eds.), Seminar on Stochastic Processes, 1989, Birkhäuser, Boston, 1990, 1-16.
    • (1990) Seminar on Stochastic Processes , pp. 1-16
    • Bass, R.F.1    Burdzy, K.2
  • 3
    • 84963057298 scopus 로고
    • The boundary Harnack principle for non-divergence form elliptic operators
    • _, _, The boundary Harnack principle for non-divergence form elliptic operators, J. London Math. Soc. 50 (1994), 157-169.
    • (1994) J. London Math. Soc. , vol.50 , pp. 157-169
  • 5
    • 0010682521 scopus 로고
    • Markov processes and their potential theory
    • Academic Press, New York
    • R. M. Blumenthal and R. K. Getoor, Markov Processes and Their Potential Theory, Pure and Appl. Math., Academic Press, New York, 1968.
    • (1968) Pure and Appl. Math.
    • Blumenthal, R.M.1    Getoor, R.K.2
  • 6
    • 0003456233 scopus 로고
    • Multidimensional brownian excursions and potential theory
    • Longman, Harlow
    • K. Burdzy, Multidimensional Brownian Excursions and Potential Theory, Pitman Res. Notes in Math. 164, Longman, Harlow, 1987.
    • (1987) Pitman Res. Notes in Math. , vol.164
    • Burdzy, K.1
  • 7
    • 0000736848 scopus 로고
    • Boundary behavior of nonnegative solutions of elliptic operators in divergence form
    • L. Caffarelli, E. Fabes, S. Mortola, and S. Salsa, Boundary behavior of nonnegative solutions of elliptic operators in divergence form, Indiana Univ. Math. J. 30 (1981), 621-640.
    • (1981) Indiana Univ. Math. J. , vol.30 , pp. 621-640
    • Caffarelli, L.1    Fabes, E.2    Mortola, S.3    Salsa, S.4
  • 8
    • 84966211299 scopus 로고
    • Conditional gauge, and potential theory for the schrödinger operator
    • M. Cranston, E. Fabes, and Z. Zhao, Conditional gauge, and potential theory for the Schrödinger operator, Trans. Amer. Math. Soc. 307 (1988), 171-194.
    • (1988) Trans. Amer. Math. Soc. , vol.307 , pp. 171-194
    • Cranston, M.1    Fabes, E.2    Zhao, Z.3
  • 9
    • 0017727486 scopus 로고
    • Estimates of harmonic measure
    • B. Dahlberg, Estimates of harmonic measure, Arch. Rational Mech. Anal. 65 (1977), 275-288.
    • (1977) Arch. Rational Mech. Anal. , vol.65 , pp. 275-288
    • Dahlberg, B.1
  • 10
    • 0004188078 scopus 로고
    • Academic Press, New York
    • E. B. Dynkin, Markov Processes, Vols. I, II, Academic Press, New York, 1965.
    • (1965) Markov Processes , vol.1-2
    • Dynkin, E.B.1
  • 11
    • 0002004980 scopus 로고
    • Boundary behavior of harmonic functions in non-tangentially accessible domains
    • D. S. Jerison and C. E. Kenig, Boundary behavior of harmonic functions in non-tangentially accessible domains, Adv. in Math. 46 (1982), 80-147.
    • (1982) Adv. in Math. , vol.46 , pp. 80-147
    • Jerison, D.S.1    Kenig, C.E.2
  • 14
    • 0001446809 scopus 로고
    • Infinitely divisible processes and their potential theory
    • S. C. Port and C. J. Stone, Infinitely divisible processes and their potential theory, Ann. Inst. Fourier (Grenoble) 21 (2) (1971), 157-275; 21 (4) (1971), 179-265.
    • (1971) Ann. Inst. Fourier (Grenoble) , vol.21 , Issue.2 , pp. 157-275
    • Port, S.C.1    Stone, C.J.2
  • 15
    • 0001446809 scopus 로고
    • S. C. Port and C. J. Stone, Infinitely divisible processes and their potential theory, Ann. Inst. Fourier (Grenoble) 21 (2) (1971), 157-275; 21 (4) (1971), 179-265.
    • (1971) Ann. Inst. Fourier (Grenoble) , vol.21 , Issue.4 , pp. 179-265
  • 16
    • 84972537495 scopus 로고
    • On stable processes with boundary conditions
    • S. Watanabe, On stable processes with boundary conditions, J. Math. Soc. Japan 14 (1962), 170-198.
    • (1962) J. Math. Soc. Japan , vol.14 , pp. 170-198
    • Watanabe, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.