Meyer's topology and brownian motion in a composite medium

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1. [1] M. Biroli and U. Mosco, "Dirichlet forms and structural estimates in discontinuous media,", C.R.Acad.Sci.Paris, t. 313, Sery I, (1991); Zbl0760.49004MR1133491
2. [2] M. Biroli and U. Mosco, "Discontinuous media and Dirichlet forms of diffusion type", Developments in Partial Differential Equations and Applications to Math. Physics, Plenum Press, New York, (1992); Zbl0893.31008MR1213919
3. [3] Z. Chen, "On reflecting diffusion processes and Skorohod decompositions", Prob. Theory and Related Fields, Vol.94, No.3, (1993), 281-315; Zbl0767.60074MR1198650
4. [4] Z. Chen, P. Fitzsimmons and R. Williams, "Reflecting Brownian motions: quasimartingales and strong caccioppoli sets", Potential Analysis2 (1993), p.219-243; Zbl0812.60065MR1245240
5. [5] C.M. Elliott and H.R. Ockendon, Weak and Variational Methods for Moving Boundary Problems, Pitman Publishing Inc. (1982); Zbl0476.35080MR650455
6. [6] M. Fukushima, Dirichlet forms and Markov Processes, North-Holland, (1985); Zbl0422.31007MR569058
7. [7] L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, (1992); Zbl0804.28001MR1158660
8. [8] T. Funaki, "A certain class of diffusion processes associated with nonlinear parabolic equations," Z.Wahrsch. verw. Gebiete, 67, (1984); Zbl0546.60081MR762085
9. [9] J.M. Hill and J.N. Dewynne, Heat Conduction, Blackwell Scientific Publications, (1987); Zbl0656.35001MR938300
10. [10] T.G. Kurtz, "Random time changes and convergence in distribution under the Meyer-Zheng conditions", the Annals of Prob., (1991), V19, No.3, 1010-1034; Zbl0742.60036MR1112405
11. [11] O.A. Ladyzenskaya, V.A. Solonnikov and N.N. Uralceva, Linear and Quasilinear Equations of Parabolic Type, AMS, (1968); 
12. [12] A.V. Luikov, Analytical Heat Diffusion Theory, Academic Press, (1968); 
13. [13] T. Lyons and T.S. Zhang, "Note on convergence of Dirichlet processes", Bull. London Math. Soc.25 (1993), 353-356; Zbl0793.31006MR1222728
14. [14] T. Lyons and W. Zheng, "A Crossing estimate for the canonical process on a Dirichlet space and a tightness result" , Colloque Paul Levy sur les Processus Stochastiques, Asterisque157-158 (1988), 249-271; Zbl0654.60059MR976222
15. [15] T. Lyons and W. Zheng, "Diffusion Processes with Non-smooth Diffusion Coefficients and Their Density Functions", the Proceedings of Edinburgh Mathematical Society, (1990), 231-242; Zbl0715.60096MR1069519
16. [16] P.A. Meyer and W. Zheng, "Tightness criteria for laws of semimartingales," Ann. Inst. Henri Poincaré. 20 (1984), No. 4, 357-372; Zbl0551.60046MR771895
17. [17] M.N., Özisik, Heat Conduction, 2nd ed., John Wiley & Sons, Inc. (1993); 
18. [18] J. Nash, "Continuity of solutions of parabolic and elliptic equations", Amer. J. Math., (1958), 80, 931-954; Zbl0096.06902MR100158
19. [19] M. Takeda, "Tightness property for symmetric diffusion processes"Proc. Japan Acad. Ser.A, Math. Sci. , (1988), 64; Zbl0667.60077MR952808
20. [20] T. Uemura, "On weak convergence of diffusion processes generated by energy forms", Preprint, 1994; Zbl0852.60090MR1380730
21. [21] R.J. Williams and W.A. Zheng, "On reflecting Brownian motion — a weak convergence approach, "A. Inst. H. Poincare, (1990), 26, No.3, p.461-488; Zbl0704.60081MR1066089
22. [22] W. Zheng, "Tightness results for laws of diffusion processes application to stochastic machanics, "A. Inst. H. Poincare, (1985), 21; Zbl0579.60050MR798890
23. [23] W. Zheng, "Conditional propagation of chaos and a class of quasi-linear PDE", Annals of Probobability, (1965), Vol.23, No.3, 1389-1413. Zbl0836.60053MR1349177