Comparison of Green Functions for Generalized Schrodinger Operators on $C^{1,1}$-Domains

Volume 4, Issue 1, 2003

Article 22

COMPARISON OF GREEN FUNCTIONS FOR GENERALIZED SCHRÖDINGER OPERATORS ON C^1,1-DOMAINS

DEPARTMENT OF MATHEMATICS,
FACULTY OF SCIENCES OF TUNIS,
CAMPUS UNIVERSITAIRE 1060
TUNIS, TUNISIA.
E-Mail: Lotfi.Riahi@fst.rnu.tn

Received 16 September, 2002; Accepted 10 February, 2003.
Communicated by: A.M. Fink

ABSTRACT. We establish some inequalities on the ${\frac{1}{2}}\Delta$ -Green function

on bounded $C^{1,1}$ -domain. We use these inequalities to prove the existence of the $\left( {\frac{1}{2}}\Delta -\mu \right)$ -Green function $G_{\mu }$ and its comparability to

, where $\mu$ is in some general class of signed Radon measures. Finally we prove that the choice of this class is essentially optimal.

Key words:
Green function, Schrödinger operator, 3G-Theorem.

2000 Mathematics Subject Classification:
34B27, 35J10.

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