Gradient estimates for harmonic and q-harmonic functions of symmetric stable processes

Illinois Journal of Mathematics

Volumn 46, Issue 2, 2002, Pages 541-556

  Bogdan, K ^a   Kulczycki, T ^a,b   Nowak, A ^a  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

^b Polish Academy of Sciences   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036628268     PISSN: 00192082     EISSN: None     Source Type: Journal    
DOI: 10.1215/ijm/1258136210     Document Type: Article

References (19)

1. R. Bañuelos and M.H. Pang, Lower bound gradient estimates for solutions of Schrödinger equations and heat kernels, Comm. Partial Differential Equations 24 (1999), 499-543.
2. R.M. Blumenthal, and R.K. Getoor, Markov processes and potential theory, Springer, New York, 1968.
3. R.M. Blumenthal, R.K. Getoor, and D.B. Ray, On the distribution of first hits for the symmetric stable process, Trans. Amer. Math. Soc. 99 (1961), 540-554.
4. K. Bogdan, The boundary Harnack principle for the fractional Laplacian, Studia Math. 123 (1997), 43-80.
5. - Representation of α-harmonic functions in Lipschitz domains, Hiroshima Math. J. 29 (1999), 227-243.
6. - Sharp estimates for the Green function of Lipschitz domains, J. Math. Anal. Appl. 243 (2000), 326-337.
7. K. Bogdan and T. Byczkowski, Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains, Studia Math. 133 (1999), 53-92.
8. - Potential theory of Schrödinger operators based on fractional Laplacian, Probab. Math. Statist. 20 (2000), 293-335.
9. 1,α, Rev. Mat. Iber. 3 (1987), 139-162.
10. Z.Q. Chen and R. Song, Estimates on Green functions and Poisson kernels for symmetric stable process, Math. Ann. 312 (1998), 465-501.
11. - Intrinsic ultracontractivity and conditional gauge for symmetric stable processes, J. Funct. Anal. 150 (1997), 204-239.
12. - Intrinsic ultracontractivity, conditional lifetimes and conditional gauge for symmetric stable processes on rough domains, Illinois J. Math. 44 (2000), 138-160.
13. M. Cranston and Z. Zhao, Some regularity results and eigenfunction estimates for the Schrödinger operator, Diffusion processes and related problems in analysis, I (Evanston, IL, 1989), Progr. Probab., vol. 22, Birkhäuser Boston, Boston, MA, 1990, pp. 139-146.
14. N. Ikeda and S. Watanabe, On some relations between the harmonic measure and the Lévy measure for a certain class of Markov processes, J. Math. Kyoto Univ. 2 (1962), 79-95.
15. T. Kulczycki, Properties of Green function of symmetric stable process, Probab. Math. Statist. 17 (1997), 339-364.
16. Exit time and Green function of cone for symmetric stable processes, Probab. Math. Statist. 19 (1999), 337-374.
17. N.S. Landkof, Foundations of modern potential theory, Springer, New York, 1972.
18. P.J. Méndez-Hernández, Exit times from cones in Rn of stable symmetric processes, Illinois J. Math. 46 (2002), 155-163.
19. K.O. Widman, Inequalities for the Green function and boundary continuity of the gradient of solutions of elliptic differential equations, Math. Scand. 21 (1967), 17-37.