A multidirectional Dirichlet problem

Journal of Geometric Analysis

Volumn 13, Issue 3, 2003, Pages 495-520

  Verchota, Gregory C ^a   Vogel, Andrew L ^a  

^a SYRACUSE UNIVERSITY   (United States)

Author keywords

Complexes; Curtis Zeeman manifold; Lipschitz; Mazur manifold; NTA; PL; polyhedron; reverse H lder

Indexed keywords

EID: 84867963270     PISSN: 10506926     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02922056     Document Type: Article

References (39)

1. Bing, R.H.Some Aspects of the Topology of 3-ManifoldsRelated to the Poincaré Conjecture, Lectures on modern mathematics, Vol. II, John Wiley & Sons, New York, (1964), 93-128. MR 30 #2474.
2. Bing, R.H. The geometric topology of 3-manifolds, American Mathematical Society Colloquium Publications, Vol. 40,AMS, (1983).
3. J.W. Cannon 1979 Shrinking cell-like decompositions of manifolds, Codimension three Ann. Math. (2) 110 1 83 112 10.2307/1971245 541330
4. R.R. Coifman G. Weiss 1977 Extensions of hardy spaces and their use in analysis Bull. Am. Math. Soc. 83 4 569 645 0358.30023 10.1090/S0002-9904-1977- 14325-5 447954
5. M.L. Curtis E.C. Zeeman 1960 On the polyhedral Schoenflies theorem Proc. Am. Math. Soc. 11 888 889 10.2307/2034432 119208
6. B.E.J. Dahlberg 1977 Estimates of harmonic measure Arch. Rational Mech. Anal. 65 3 275 288 0406.28009 466593 10.1007/BF00280445
7. 1-domains Studia Math. 66 1 13 24 0422.31008 562447
8. p for Laplace's equation in Lipschitz domains Ann. Math. (2) 125 3 437 465 10.2307/1971407 890159
9. Dugundji,Topology, Allyn and Bacon, (1966).
10. 1 domains Acta Math. 141 165 186 0402.31009 10.1007/BF02545747 501367
11. p spaces of several variables Acta Math. 129 137 193 0257.46078 10.1007/BF02392215 447953
12. Glaser, L.C.Geometrical Combinatorial Topology, Vol. I, Van Nostrand Reinhold, (1970).
13. Helms, L.L.Introduction to Potential Theory, Wiley-Interscience, (1969).
14. Hurewicz, W. and Wallman, H.Dimension Theory, Princeton University Press, (1941).
15. R.A. Hunt R.L. Wheeden 1968 On the boundary values of harmonic functions Trans. Am. Math. Soc. 132 307 322 0159.40501 10.2307/1994842 226044
16. R.A. Hunt R.L. Wheeden 1970 Positive harmonic functions on Lipschitz domains Trans. Am. Math. Soc. 147 507 527 0193.39601 10.2307/1995208 274787
17. D.S. Jerison C.E. Kenig 1982 Boundary behavior of harmonic functions in nontangentially accessible domains Adv. in Math. 46 80 147 0514.31003 10.1016/0001-8708(82)90055-X 676988
18. D.S. Jerison C.E. Kenig 1982 Boundary value problems on lipschitz domains, MAA Studies in Mathematics Stud. Part. Diff. Eq. 23 1 68 716504
19. P.W. Jones 1982 A geometric localization theorem Adv. in Math. 46 1 71 79 0515.31004 10.1016/0001-8708(82)90054-8 676987
20. Kenig, C.E. Harmonic analysis techniques for second order elliptic boundary value problems,AMS, (1994).
21. Kirby and Lickorish, personal communication, (2001).
22. J. Král W. Wendland 1986 Some examples concerning applicability of the Fredholm-Radon method in potential theory Apl. Mat. 31 4 293 308 0615.31005 854323
23. B. Mazur 1961 A note on some contractible 4-manifolds Ann. Math. 73 1 221 228 10.2307/1970288 125574
24. Mitchinson, D.Celebrating Moore, University of California Press, (1998).
25. Moise, E.E.Geometric Topology in Dimensions 2 and 3, Springer-Verlag, (1977).
26. J. Nečas 1962 Sur les domaines du type N Czechoslovak Math. J. 12 274 287 152734
27. J. Pipher G.C. Verchota 1995 Dilation invariant estimates and the boundary Garding inequality for higher order elliptic operators Ann. Math. 142 1 38 0878.35035 10.2307/2118610 1338674
28. Rourke, C.P. and Sanderson,B. J. Introduction to Piecewise-Linear Topology, Springer-Verlag, (1972).
29. M.E. Rudin 1958 An unshellable triangulation of a tetrahedron Bull. Am. Math. Soc. 64 90 91 0082.37602 10.1090/S0002-9904-1958-10168-8 97055
30. Rushing, T.B.Topological Embeddings, Academic Press, (1983).
31. S. Semmes 1996 Good metric spaces without good parameterizations Rev. Mat. Iberoamericana 12 1 187 275 0854.57018 1387590
32. Siebenmann, L. and Sullivan, D. On complexes that are Lipschitz manifolds, Geometric topology, (Proc. Georgia Topology Conf., Athens, Ga., 1977), Academic Press, New York, 503-525, (1979). MR 80h:57027.
33. Stein, E.M.Singular Integrals and Differentiability Properties of Functions, Princeton University Press, (1970).
34. Thurston, W.P.Three-Dimensional Geometry and Topology, Princeton University Pres, (1997).
35. G.C. Verchota 1984 Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains J. Funct. Anal. 59 3 572 611 0589.31005 10.1016/0022-1236(84)90066-1 769382
36. Verchota, G.C. The use of Rellich identities on certain nongraph boundaries, Harmonic analysis and boundary value problems, (Fayetteville, AR, 2000),Am. Math. Soc., Providence, RI, 127-138, (2001). MR 1 840 431
37. 4, in progress, (2002).
38. Yemelichev, V.A., Kovalev, M.M., and Kravstov, M.K.Polytopes, Graphs, and Optimization, Cambridge University Press, (1984).
39. G.M. Ziegler 1998 Shelling polyhedral 3-balls and 4-polytopes Disc. Comput. Geom. 19 2 159 174 0898.52006 10.1007/PL00009339 1600042