Asymptotics and continuity properties near infinity of solutions of Schrödinger equations in exterior domains

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1. [1] L. Bers, Local behaviour of solutions of general elliptic equations. Comm. Pure Appl. Math., t. 8, 1955, p. 473-496. Zbl0066.08101MR75416
2. [2] J. Boman, Differentiability of a function and of its composition with functions of one variable. Math. Scand., t. 20, 1967, p. 249-268. Zbl0182.38302MR237728
3. [3] L.A. Cafarelli and A. Friedman, Partial regularity of the zero-set of solutions of linear and superlinear elliptic equations. J. Differ. Equations, t. 60, 1985, p. 420- 433. Zbl0593.35047MR811775
4. [4] S.Y. Cheng, Eigenfunctions and nodal sets. Comment. Math. Helvetici, t. 51, 1976, p. 43-55. Zbl0334.35022MR397805
5. [5] A. Erdélyi, W. Magnus, F. Oberhettinger, F.G. Tricomi, Bateman manuscript project : higher transcendental functions, vol. II, McGraw Hill, New York, Toronto, London, 1953. Zbl0052.29502MR66496
6. [6] R. Froese and I. Herbst, Patterns of exponential decay for solutions to second order elliptic equations in a sector of R2, to appear in J. d'Analyse Math. Zbl0657.35047
7. [7] D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, Springer Verlag, Berlin, Heidelberg, New York. 1977. Zbl0361.35003MR473443
8. [8] I. Herbst, Lower bounds in cones for solutions to the Schrödinger equation, J. d'Analyse Math., t. 47, 1986, p. 151-174. Zbl0627.35022MR874048
9. [9] M. Hoffmann-Ostenhof, Asymptotics of the nodal lines of solutions of 2-dimensional Schrödinger equations, submitted for publication. Zbl0627.35024
10. [10] M. Hoffmann-Ostenhof and T. Hoffmann-Ostenhof, On the asymptotics of nodes of L2-solutions of Schrödinger equations, in preparation. Zbl0658.35021
11. [11] M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and B. Simon, Brownian motion and a consequence of Harnack's inequality: nodes of quantum wave functions. Proc. Amer. Math. Soc., t. 80, 1980, p. 301-305. Zbl0444.35024MR577764
12. [12] M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and J. Swetina, Pointwise bounds on the asymptotics of spherically averaged L2-solutions of one-body Schrödinger equations. Ann. Inst. H. Poincaré, t. 42, 1985, p. 341-361. Zbl0595.35033MR801233
13. [13] M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and J. Swetina, Continuity and nodal properties near infinity for solutions of 2-dimensional Schrödinger equations. Duke Math. J., t. 53, 1986, p. 271-306. Zbl0599.35036MR835810
14. [14] J. Mujica, Complex analysis in Banach spaces, North-Holland Mathematics Studies, t. 120, 1986, chapter 1. Zbl0586.46040MR842435
15. [15] M.H. Protter and H.F. Weinberger, Maximum principles in differential equations, Prentice Hall, Englewood Cliffs, 1967. Zbl0153.13602MR219861
16. [16] E.M. Stein, Singular integrals and differentiability of functions, Princeton University Press, Princeton, NJ, 1970. Zbl0207.13501MR290095
17. [17] D.W. Thoe, Lower bounds for solutions of perturbed Helmholtz equations in exterior regions. J. Math. Anal. Appl., t. 102, 1984, p. 113-122. Zbl0552.35015MR751346

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