We show that the Kerzman-Stein operator associated to a bounded planar domain Ω with C1-boundary is compact in L2(bΩ). We establish the Kerzman-Stein equation for the Szego projection associated to a bounded planar domain with Lipschitz boundary. As an application, we extend to the Lipschitz setting a theorem of S. Bell for representing the solution of the classical Dirichlet problem on a simply connected bounded domain in the complex plane.
Szego projection versus potential theory for non-smooth planar domains / Lanzani L.. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - ELETTRONICO. - 48:2(1999), pp. 537-555. [10.1512/iumj.1999.48.1631]
Szego projection versus potential theory for non-smooth planar domains
Lanzani L.
1999
Abstract
We show that the Kerzman-Stein operator associated to a bounded planar domain Ω with C1-boundary is compact in L2(bΩ). We establish the Kerzman-Stein equation for the Szego projection associated to a bounded planar domain with Lipschitz boundary. As an application, we extend to the Lipschitz setting a theorem of S. Bell for representing the solution of the classical Dirichlet problem on a simply connected bounded domain in the complex plane.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.