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  1. R. Banuelos and K. Burdzy. On the ``hot spots'' conjecture of J. Rauch J. Funct. Anal. 164, 1--33 (1999) Math. Review 2000m:35085
  2. R. F. Bass. Probabilistic Techniques in Analysis Series of Prob. Appl. (1995) Math. Review 96e:60001
  3. R. F. Bass and K. Burdzy. Fiber Brownian motion and the ``hot spots'' problem Duke Math. J. 105 (2000), no. 1, 25--58. Math. Review 2001g:60190
  4. R. F. Bass and P. Hsu. Some potential theory for reflecting Brownian motion in Holder and Lipschitz domains Ann. Prob. Vol. 19 No. 2 486--508 (1991) Math. Review 92i:60142
  5. K. Burdzy and W. Werner. A counterexample to the ``hot spots'' conjecture Ann. Math. 149 309--317 (1999) Math. Review 2000b:35044
  6. M. Cranston and Y. Le Jan. Noncoalescence for the Skorohod equation in a convex domain of R^2 Probab. Theory Related Fields 87, 241--252 (1990) Math. Review 92e:60116
  7. E. B. Davies. Heat Kernels and Spectral Theory Cambridge University Press, 1989. Math. Review 92a:35035
  8. P. Dupuis and H. Ishii. On Lipschitz continuity of the solution mapping to the Skorokhod problem, with applications Stochastics and Stochastics Reports, Vol. 35, pp. 31--62 (1991) Math. Review 93e:60110
  9. P. Dupuis and K. Ramanan. Convex duality and the Skorokhod Problem. I, II Probab. Theory Related Fields 115 (1999), no. 2, 153--195, 197--236. Math. Review 2001f:49041
  10. D. Jerison and N. Nadirashvili. The ``hot spots'' conjecture for domains with two axes of symmetry J. Amer. Math. Soc. 13 (2000), no. 4, 741--772 Math. Review 2001f:35110
  11. B. Kawohl. Rearrangements and Convexity of Level Sets in PDE Lecture Notes in Mathematics, Vol. 1150 (1985) Math. Review 87a:35001
  12. M. A. Krasnosel'skij, Je. A. Lifshits and A. V. Sobolev. Positive Linear Systes: The Method of Positive Operators Sigma Series in Appl. Math. Vol. 5 (1989) Math. Review 91f:47051
  13. O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Ural'ceva. Linear and Quasilinear Equations of Parabolic Type Transl. Math. Monogr., Vol. 23, AMS, Providence (1968) Math. Review 39:3159b
  14. P. L. Lions and A. S. Sznitman. Stochastic differential equations with reflecting boundary conditions Comm. Pure appl. Math. Vol. 37, 511--537 (1984) Math. Review 85m:60105
  15. D. Lupo and A. M. Micheletti. On the persistence of the multiplicity of eigenvalues for some variational elliptic operator depending on the domain J. Math. Anal. Appl. 193 no. 3 990--1002 (1995) Math. Review 96h:35032
  16. N. S. Nadirashvili. On the multiplicity of the eigenvalues of the Neumann problem Soviet Math. Dokl. 33 281--282 (1986) Math. Review 88a:35068

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