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2, 447–460. [3] J. E. Brothers, W. P. Ziemer, Minimal rearrangements of Sobolev functions, 15th winter school in abstract analysis (Srn´ı, 1987), Acta Univ. Carolin. Math. Phys, 28 (1987), no. 2, 13–24. [4] F. -Q. Wang, Nonlinear elliptic equations on expanding symmetric domains, J. Differential Equations, 156 (1999), no. 1, 153–181. [5] F. -Q. Wang, On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existence (and nonexistence), and symmetry of extremal functions, Comm. Pure Appl.

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27] M. Struwe, Variational Methods and Applications to Nonlinear Partial Differential Equations and Hamiltonian systems, Springer-Verlag, Berlin/New York (1990). [28] S. Terracini, On positive entire solutions to a class of equations with singular coefficient and critical exponent, Adv. Diff. , 1 (1996), no. 2, 241–264. -Q. Wang, Existence and symmetry of multi-bump solutions for nonlinear Schrdinger equations, J. Differential Equations, 159 (1999), no. 1, 102–137. [30] M. Willem, Minimax theorems, Progress in Nonlinear Differential Equations and their Applications, 24.

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Zero-crossings and noise supression in auditory wavelet transformations by Wang Shamma

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