Asymptotics and continuity properties near infinity of solutions of Schrödinger equations in exterior domains
Hoffmann-Ostenhof, Maria ; Hoffmann-Ostenhof, Thomas ; Swetina, Jörg
Annales de l'I.H.P. Physique théorique, Tome 47 (1987), p. 247-280 / Harvested from Numdam
@article{AIHPA_1987__46_3_247_0,
     author = {Hoffmann-Ostenhof, Maria and Hoffmann-Ostenhof, Thomas and Swetina, J\"org},
     title = {Asymptotics and continuity properties near infinity of solutions of Schr\"odinger equations in exterior domains},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {47},
     year = {1987},
     pages = {247-280},
     mrnumber = {892365},
     zbl = {0641.35017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1987__46_3_247_0}
}
Hoffmann-Ostenhof, Maria; Hoffmann-Ostenhof, Thomas; Swetina, Jörg. Asymptotics and continuity properties near infinity of solutions of Schrödinger equations in exterior domains. Annales de l'I.H.P. Physique théorique, Tome 47 (1987) pp. 247-280. http://gdmltest.u-ga.fr/item/AIHPA_1987__46_3_247_0/

[1] L. Bers, Local behaviour of solutions of general elliptic equations. Comm. Pure Appl. Math., t. 8, 1955, p. 473-496. | MR 75416 | Zbl 0066.08101

[2] J. Boman, Differentiability of a function and of its composition with functions of one variable. Math. Scand., t. 20, 1967, p. 249-268. | MR 237728 | Zbl 0182.38302

[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. | MR 811775 | Zbl 0593.35047

[4] S.Y. Cheng, Eigenfunctions and nodal sets. Comment. Math. Helvetici, t. 51, 1976, p. 43-55. | MR 397805 | Zbl 0334.35022

[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. | MR 66496 | Zbl 0052.29502

[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. | Zbl 0657.35047

[7] D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, Springer Verlag, Berlin, Heidelberg, New York. 1977. | MR 473443 | Zbl 0361.35003

[8] I. Herbst, Lower bounds in cones for solutions to the Schrödinger equation, J. d'Analyse Math., t. 47, 1986, p. 151-174. | MR 874048 | Zbl 0627.35022

[9] M. Hoffmann-Ostenhof, Asymptotics of the nodal lines of solutions of 2-dimensional Schrödinger equations, submitted for publication. | Zbl 0627.35024

[10] M. Hoffmann-Ostenhof and T. Hoffmann-Ostenhof, On the asymptotics of nodes of L2-solutions of Schrödinger equations, in preparation.

[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. | MR 577764 | Zbl 0444.35024

[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. | Numdam | MR 801233 | Zbl 0595.35033

[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. | MR 835810 | Zbl 0599.35036

[14] J. Mujica, Complex analysis in Banach spaces, North-Holland Mathematics Studies, t. 120, 1986, chapter 1. | MR 842435 | Zbl 0586.46040

[15] M.H. Protter and H.F. Weinberger, Maximum principles in differential equations, Prentice Hall, Englewood Cliffs, 1967. | MR 219861 | Zbl 0153.13602

[16] E.M. Stein, Singular integrals and differentiability of functions, Princeton University Press, Princeton, NJ, 1970. | MR 290095 | Zbl 0207.13501

[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. | MR 751346 | Zbl 0552.35015