Normalized solutions of Schrödinger equations with potentially bounded measures

Hansen W (2004)
Potential Analysis 21(2): 99-135.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Abstract / Bemerkung
Given a potentially bounded signed measure mu on a Brelot space (X, H) with Green function G, it is well known that mu-harmonic functions (i.e., in the classical case, finely continuous versions of solutions to Deltau- umu = 0) may be very discontinuous. In this paper it is shown that under very general assumptions on G ( satisfied for large classes of elliptic second-order linear differential operators) normalized perturbation, however, leads to a Brelot space (X, (H) over tilde (mu)) admitting a Green function T-mu(G) which is locally ( or even globally) comparable with G and has all properties required of G before. In particular, iterated perturbation is possible. Moreover, intrinsic Holder continuity of quotients of harmonic functions with respect to the local quasimetric rho:= (G(-1) + * G(-1))/ 2 yields rho-Holder continuity for quotients of mu-harmonic functions as well.
Stichworte
Green function; perturbation; Schrodinger operator; Holder continuity
Erscheinungsjahr
2004
Zeitschriftentitel
Potential Analysis
Band
21
Ausgabe
2
Seite(n)
99-135
ISSN
0926-2601
Page URI
https://pub.uni-bielefeld.de/record/1607974

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Hansen W. Normalized solutions of Schrödinger equations with potentially bounded measures. Potential Analysis. 2004;21(2):99-135.
Hansen, W. (2004). Normalized solutions of Schrödinger equations with potentially bounded measures. Potential Analysis, 21(2), 99-135. doi:10.1023/B:POTA.0000025378.97262.f3
Hansen, W. (2004). Normalized solutions of Schrödinger equations with potentially bounded measures. Potential Analysis 21, 99-135.
Hansen, W., 2004. Normalized solutions of Schrödinger equations with potentially bounded measures. Potential Analysis, 21(2), p 99-135.
W. Hansen, “Normalized solutions of Schrödinger equations with potentially bounded measures”, Potential Analysis, vol. 21, 2004, pp. 99-135.
Hansen, W.: Normalized solutions of Schrödinger equations with potentially bounded measures. Potential Analysis. 21, 99-135 (2004).
Hansen, Wolfhard. “Normalized solutions of Schrödinger equations with potentially bounded measures”. Potential Analysis 21.2 (2004): 99-135.