Integration by parts formula for regional fractional Laplacian

Communications in Mathematical Physics

Volumn 266, Issue 2, 2006, Pages 289-329

  Guan, Qing Yang ^a  

^a INSTITUTE OF APPLIED MATHEMATICS   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746215057     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-006-0054-9     Document Type: Article

References (18)

1. Bass, R.F.: Probabilistic Techniques in Analysis. New York: Springer, 1995
2. Bogdan, K., Burdzy, K., Chen, Z.Q.: Censored stable processes. Probab. Theory Relat. Fields 127, 89-152 (2003)
3. Bogdan, K., Byczkowski, T.: Potential theory for the α-stable Schr̈dinger operator on bounded Lipschitz domains. Studia Math 133(1), 53-92 (1999)
4. Chandrasekhar, S.: Stochastic problems in Physics and Astronomy. Rev. Mod. Phys. 15, 1-89 (1943)
5. Chen, Z.Q., Kim, P.: Green function estimates for censored stable processes. Probab. Theory Relat. Fields 124, 295-610 (2002)
6. Chen, Z.Q., Kumagai, T.: Heat Kernel Estimates for Stable-like Process on d-Sets. Stochastic Process Appl. 108, 27-62 (2003)
7. Fukushima, M., Oshima, Y., Takeda, M.: Dirichlet Form and Symmetric Markov Processes. Berlin: Walter de Gruyter, 1994
8. Gilbarg, D., Trudinger, N.: Elliptic Partial Differential Equations of Second order. 2nd edition, Berlin-Heidelberg-New York: Springer-Verlag, 1983
9. Guan, Q. Y. : Reflecting α-Symmetric Stable Processes and Power Laplace Operators. Doctor Dissertation, Institute of Applied Mathematics, Academy of Mathematics and System Sciences, CAS, 2003
10. Guan, Q.Y., Ma, Z.M.: The reflected α-symmetric stable processes and regional fractional Laplacian. Probab. Theory Relat. Fields 134(4), 649-694 (2006)
11. Guan, Q.Y., Ma, Z.M.: Boundary value problems for fractional Laplacian. Stoch. and Dyn. 5(3), 385-424 (2005)
12. Jacob, N., Schiling, R.: Some Dirichlet spaces obtained by subordinate reflected diffusions. Rev. Mat. Iberoamericanna, 15, 59-91 (1999)
13. Klafter, J., Shlesiger, M.F., Zumofen, G.: Beyond Brownian motion. Physics Today, 49, 33-39 (1996)
14. Landkof, N.S.: Foundations of Modern Potential Theory. New York: Springer, 1972
15. Li, Y.Y., Nirenberg, L.: The Dirichlet problem for singularly perturbed elliptic equations. Comm. Pure Appl. Math. 51(11-12), 1445-1490 (1998)
16. Metzler, R., Klafter, J.: The Random Walks Guide to Anomalous Diffusion: A Fractional Dynamics Approach. Phys. Rep. 339, 1-77 (2000)
17. Solomon, T.H., Weeks, E.R., Swinney, H.L.: Observation of anomalous diffusion and Lévy flights in a two-dimensional rotating flow. Phys. Rev. Lett. 71, 3975-3978 (1993)
18. Stein, E.M.: Singular integrals and differentiability properties of functions. Princeton, NJ: Princeton Univ. Press, 1970