Interior Hölder estimates for solutions of Schrödinger equations and the regularity of nodal sets

 Access to full text

 Full (PDF)

1. [A] G. Alessandrini, Singular solutions and the determination of conductivity by boundary measurements, J. Diff. Equ. 84 (1990), 252-272. Zbl0778.35109MR91e:35210
2. [AS] M. Aizenman, B. Simon, Brownian motion and Harnack inequality for Schrödinger operators, Commun. Pure Appl. Math. 35 (1982), 209-273. Zbl0459.60069MR84a:35062
3. [B] L. Bers, Local behaviour of solutions of general linear elliptic equations, Commun. Pure Appl. Math. 8 (1955), 473-496. Zbl0066.08101MR17,743a
4. [CF] L. A. Caffarelli, A. Friedman, Partial regularity of the zero-set of solutions of linear and superlinear elliptic equations, J. Differential Equations 60 (1985), 420-433. Zbl0593.35047MR87e:35006
5. [CM] S. Chanillo, B. Muckenhoupt, Nodal geometry on Riemannian manifolds, J. Diff. geometry 34 (1991), 85-71. Zbl0727.58048MR92f:58183
6. [D] R.-T. Dong, Nodal sets of eigenfunctions on Riemann surfaces, J. Diff. Geometry 36 (1992), 493-506. Zbl0776.53024MR93h:58159
7. [DF] H. Donelly, Ch. Fefferman, Nodal sets of eigenfunctions on Riemannian manifolds, Invent. math. 93 (1988), 161-183. Zbl0659.58047MR89m:58207
8. [GT] D. Gilbarg, N.S. Trudinger, Elliptic partial differential equations 2nd ed., Springer, Berlin, 1983. Zbl0562.35001
9. [HO2] M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, Local properties of solutions of Schrödinger equations, Commun. PDE 17 (1992), 491-522. Zbl0783.35054MR93d:35033
10. [HO2N] M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, N. Nadirashvili, Regularity of the nodal sets of solutions to Schrödinger equations, Math. Results in Quantum Mechanics, Int. Conf. in Blossin, Germany, May 17-21 1993, Ed. by M. Demuth, P. Exner, H. Neidhardt, V. Zagrebnov, p.19-25, Operator Theory:Advances and Applications, Vol. 70, Birkhäuser, Basel, 1994. Zbl0817.35019
11. [HO2N1] M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, N. Nadirashvili, Interior Hölder estimates for solutions of Schrödinger equations and the regularity of nodal sets, to be submitted (1994). Zbl0948.35501
12. [HO2S1] M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, H. Stremnitzer, electronic wavefunctions near coalescence points, Phys. Rev. Letters 68 (1992), 3857-3860. 
13. [HO2a] M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, On the local behaviour of nodes of solutions of Schrödinger equations in dimension ≥ 3, Commun. PDE 15 (1990), 435-451. Zbl0725.35005MR91f:35086
14. [HS] R. Hardt, L. Simon, Nodal sets for solutions of elliptic equations, J. Diff. Geometry 30 (1989), 505-522. Zbl0692.35005MR90m:58031
15. [K] T. Kato, Schrödinger operators with singular potentials, Is. J. Math. 13 (1973), 135-148. Zbl0246.35025MR48 #12155
16. [Ke] C. Kenig, Restriction theorems, Carleman estimates, uniform Sobolev inequalities and their application, Lecture Notes in Mathematics 1384 (1989), 69-89. Zbl0685.35003MR90m:35016
17. [KS] P. Kröger, K.-Th. Sturm, Hölder continuity of normalized solutions of the Schrödinger equation, (to appear) Math. Ann. (1994). Zbl0822.35033
18. [R] L. Robbiano, Sur les zeros des solutions d'inequalités differentielles elliptiques, Commun. PDE 12 (1987), 903-919. Zbl0654.35036MR88e:35014
19. [S] B. Simon, Schrödinger semigroups, Bull. Amer. Math. Soc. 7 (1982), 447-526. Zbl0524.35002MR86b:81001a
20. [Sa] E. Sawyer, Unique continuation for Schrödinger operators in dimension three or less, Ann. Inst. Fourier (Grenobles) 33 (1984), 189-200. Zbl0535.35007

1. M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, N. Nadirashvili, Interior Hölder estimates for solutions of Schrödinger equations and the regularity of nodal sets