Potential theory for the \(\alpha\)-stable Schrödinger operator on bounded Lipschitz domains. (English) Zbl 0923.31003

Bogdan, Krzysztof; Byczkowski, Tomasz

Stud. Math. 133, No. 1, 53-92 (1999).

The authors develop the theory of weak Schrödinger operators \(S^\alpha\) based on the fractional Laplacian \(\Delta^{\alpha/2}\), which had been introduced in connection with studies of the relativistic stability of matter. The methods used rely mostly on the theory of Markov processes, and the main result of the paper is a conditional gauge theorem.

Reviewer: R.G.Newton (Bloomington)

MSC:

31B25	Boundary behavior of harmonic functions in higher dimensions
60J50	Boundary theory for Markov processes
26A33	Fractional derivatives and integrals

Keywords:

\(\alpha\)-stable Lévy processes; \(\alpha\)-stable Feyman-Kac semi-group; weak fractional Laplacian; \(\alpha\)-stable Schrödinger operator; \(q\)-harmonic functions; conditional gauge theorem