Elliptic regularity and essential self-adjointness of Dirichlet operators on ${ℝ}^n$

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1. [1] S. Albeverio - R. Hoegh-Krohn - L. Streit, Energy forms, Hamiltonians and distorted Brownian paths, J. Math. Phys. 18 (1977), 907-917. Zbl0368.60091MR446236
2. [2] V.I. Bogachev - N.V. Krylov - M. Röckner, Regularity of invariant measures: the case of non-constant diffusion part, J. Funct. Anal. 138 (1996), 223-242. Zbl0929.60039MR1391637
3. [3] V.I. Bogachev - M. Röckner, Hypoellipticity and invariant measures of infinite dimensional diffusions, C. R. Acad. Sci. Paris Sér.1-Math.318 (1994), 553-558. Zbl0797.60062MR1270080
4. [4] V.I. Bogachev - M. Röckner, Regularity of invariant measures on finite and infinite dimensional spaces and applications, J. Funct. Anal.133 (1995), 168-223. Zbl0840.60069MR1351647
5. [5] R. Carmona, Regularity properties of Schrödinger and Dirichlet operators, J. Funct. Anal.33 (1979), 259-296. Zbl0419.60075MR549115
6. [6] P. Cattiaux - C. Léonard, Minimization of the Kullback information of diffusion processes, Ann. Inst. H. Poincaré30 (1994), 83-132. Zbl0790.60032MR1262893
7. [7] A. Eberle, Doctor-degree Thesis, Bielefeld University (1996). 
8. [8] J. Frehse, Essential self-adjointness of singular elliptic operators, Bol. Soc. Brasil. Mat. 8 (1977),87-107. Zbl0448.47029MR603282
9. [9] M. Fukushima, On a stochastic calculus related to Dirichlet forms and distorted Brownian motion, Phys. Rep. 77 (1981), 255-262. MR639031
10. [10] D. Gilbarg - N.S. Trudinger, Elliptic partial differential equations of second order, Springer, Berlin, 1977. Zbl0361.35003MR473443
11. [11] J.G. Hooton, Dirichlet forms associated with hypercontractive semigroups, Trans. Amer. Math. Soc. 253 (1979), 237-256. Zbl0424.47028MR536945
12. [12] T. Kato, Perturbation theory for linear operators, Springer-Verlag, Berlin - Heidelberg- New York, 1976. Zbl0342.47009MR407617
13. [13] O.A. Ladyz'enskaya - N.M. Ural'tseva, Linear and quasilinear elliptic equations, Academic Press, New York, 1968. Zbl0164.13002MR244627
14. [14] V.A. Liskevich - Yu. A. Semenov, Dirichlet operators: a priori estimates and the uniqueness problem, J. Funct. Anal.109 (1992), 199-213. Zbl0788.47041MR1183610
15. [15] V. Maz'ja, Sobolev spaces, Springer, Berlin, 1985. 
16. [16] M. Röckner - T.S. Zhang, Uniqueness of generalized Schrödinger operators and applications, J. Funct. Anal.105 (1992), 187-231. Zbl0779.35028MR1156676
17. [17] M. Röckner - T.S. Zhang, Uniqueness of generalized Schrödinger operators, II, J. Funct. Anal.119 (1994), 455-467. Zbl0799.35053MR1261099
18. [18] G. Stampacchia, Équations elliptiques du second ordre à coefficients discontinus, Les Presses de l'Université de Montréal, 1966. Zbl0151.15501MR251373
19. [19] W. Stannat, First order perturbations of Dirichlet operators: hexistence and uniqueness, J. Funct. Anal.141 (1996), 216-248. Zbl0911.47037MR1414378
20. [20] E. Stein, Singular integrals and the differentiability properties of functions, Princeton University Press, Princeton, N. J., 1970. Zbl0207.13501MR290095
21. [21] M. Taylor, Pseudodifferential operators, Princeton University Press, Princeton N. J., 1981. Zbl0453.47026MR618463
22. [22] H. Triebel, Theory of functions, Birkhäuser, Basel-Boston, 1983. 
23. [23] H. Triebel, Theory of function spaces II, Birkhäuser Verlag, Basel-Boston-Berlin1992. Zbl0763.46025MR1163193
24. [24] N.S. Trudinger, Linear elliptic operators with measurable coefficients, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 27 (1973), 265-308. Zbl0279.35025MR369884
25. [25] N. Wielens, The essential self-adjointness of generalized Schrödinger operators, J. Funct. Anal.61 (1985), 98-115. Zbl0564.47010

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