Interior Hölder estimates for solutions of Schrödinger equations and the regularity of nodal sets
Journées équations aux dérivées partielles (1994), article no. 13, 9 p. 
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     author = {M. Hoffmann-Ostenhof and T. Hoffmann-Ostenhof and N. Nadirashvili},
     title = {Interior {H\"older} estimates for solutions of {Schr\"odinger} equations and the regularity of nodal sets},
     booktitle = {},
     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {13},
     pages = {1--9},
     publisher = {\'Ecole polytechnique},
     year = {1994},
     zbl = {0948.35501},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/item/JEDP_1994____A13_0/}
}
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M. Hoffmann-Ostenhof; T. Hoffmann-Ostenhof; N. Nadirashvili. Interior Hölder estimates for solutions of Schrödinger equations and the regularity of nodal sets. Journées équations aux dérivées partielles (1994), article  no. 13, 9 p. https://proceedings.centre-mersenne.org/item/JEDP_1994____A13_0/

[A] G. Alessandrini, Singular solutions and the determination of conductivity by boundary measurements, J. Diff. Equ. 84 (1990), 252-272. | MR | Zbl

[AS] M. Aizenman, B. Simon, Brownian motion and Harnack inequality for Schrödinger operators, Commun. Pure Appl. Math. 35 (1982), 209-273. | MR | Zbl

[B] L. Bers, Local behaviour of solutions of general linear elliptic equations, Commun. Pure Appl. Math. 8 (1955), 473-496. | MR | Zbl

[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. | MR | Zbl

[CM] S. Chanillo, B. Muckenhoupt, Nodal geometry on Riemannian manifolds, J. Diff. geometry 34 (1991), 85-71. | MR | Zbl

[D] R.-T. Dong, Nodal sets of eigenfunctions on Riemann surfaces, J. Diff. Geometry 36 (1992), 493-506. | MR | Zbl

[DF] H. Donelly, Ch. Fefferman, Nodal sets of eigenfunctions on Riemannian manifolds, Invent. math. 93 (1988), 161-183. | MR | Zbl

[GT] D. Gilbarg, N.S. Trudinger, Elliptic partial differential equations 2nd ed., Springer, Berlin, 1983. | Zbl

[HO2] M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, Local properties of solutions of Schrödinger equations, Commun. PDE 17 (1992), 491-522. | MR | Zbl

[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. | Zbl

[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).

[HO2S1] M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, H. Stremnitzer, electronic wavefunctions near coalescence points, Phys. Rev. Letters 68 (1992), 3857-3860.

[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. | MR | Zbl

[HS] R. Hardt, L. Simon, Nodal sets for solutions of elliptic equations, J. Diff. Geometry 30 (1989), 505-522. | MR | Zbl

[K] T. Kato, Schrödinger operators with singular potentials, Is. J. Math. 13 (1973), 135-148. | MR | Zbl

[Ke] C. Kenig, Restriction theorems, Carleman estimates, uniform Sobolev inequalities and their application, Lecture Notes in Mathematics 1384 (1989), 69-89. | MR | Zbl

[KS] P. Kröger, K.-Th. Sturm, Hölder continuity of normalized solutions of the Schrödinger equation, (to appear) Math. Ann. (1994).

[R] L. Robbiano, Sur les zeros des solutions d'inequalités differentielles elliptiques, Commun. PDE 12 (1987), 903-919. | MR | Zbl

[S] B. Simon, Schrödinger semigroups, Bull. Amer. Math. Soc. 7 (1982), 447-526. | MR | Zbl

[Sa] E. Sawyer, Unique continuation for Schrödinger operators in dimension three or less, Ann. Inst. Fourier (Grenobles) 33 (1984), 189-200. | Numdam | Zbl