Global heat kernel estimates for fractional Laplacians in unbounded open sets

Probability Theory and Related Fields

Volumn 149, Issue 3-4, 2011, Pages 373-395

  Chen, Zhen Qing ^a   Tokle, Joshua ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Censored stable process; Comparison method; Fractional Laplacian; Green function; Heat kernel; Parabolic Harnack inequality; Symmetric stable process; Transition density function

Indexed keywords

EID: 79952737277     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-009-0256-0     Document Type: Article

References (14)

1. Bogdan K., Burdzy K., Chen Z.-Q.: Censored stable processes. Probab. Theory Relat. Fields 127, 89-152 (2003).
2. Bogdan, K., Grzywny, T., Ryznar, M.: Heat kernel estimates for the fractional Laplacian. Preprint. arXiv: 0905. 2626v1 (2009).
3. Bogdan, K., Grzywny, T.: Heat kernel of fractional Laplacian in cones. Colloquium Math. (to appear).
4. Blumenthal R. M., Getoor R. K., Ray D. B.: On the distribution of first hits for the symmetric stable process. Trans. Am. Math. Soc 99, 540-554 (1961).
5. Chen, Z.-Q., Kim, P., Song, R.: Heat kernel estimates for Dirichlet fractional Laplacian. J. Euro. Math. Soc. (to appear).
6. Chen Z.-Q., Kim P., Song R.: Two-sided heat kernel estimates for censored stable-like processes. Probab. Theory Relat. Fields (2009). doi: 10. 1007/s00440-008-0193-3.
7. Chen Z.-Q., Kumagai T.: Heat kernel estimates for stable-like processes on d-sets. Stoch. Proc. Appl. 108, 27-62 (2003).
8. Fabes E. B., Garofalo N., Salsa S.: A backward Harnack inequality and Fatou theorem for nonnegative solutions of parabolic equations. Illinois J. Math. 30, 536-565 (2003).
9. Grigorýan A., Saloff-Coste L.: Dirichlet heat kernel in the exterior of a compact set. Comm. Pure Appl. Math. 55, 93-133 (2002).
10. Gyrya, P., Saloff-Coste, L.: Neumann and Dirichlet heat kernels in inner uniform domains. Preprint (2008).
11. Siudeja B.: Symmetric stable processes on unbounded domains. Pot. Anal. 25, 371-386 (2006).
12. 1, 1 functions. Glasnik Matematicki 39, 273-286 (2004).
13. Zhang Q. S.: The boundary behavior of heat kernels of Dirichlet Laplacians. J. Differ. Equ. 182, 416-430 (2002).
14. Zhang Q. S.: The global behavior of heat kernels in exterior domains. J. Funct. Anal. 200, 160-176 (2003).