Sharp estimates of the curvature of some free boundaries in two dimensions
2003 (English)In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, Vol. 28, no 1, 123-142 p.Article in journal (Refereed) Published
We prove that the Cauchy transform of a positive measure on the interval )-1,1) subset of R in the complex plane maps the exterior of the unit disc onto a domain Omega subset of C which can be written as a union of discs centered on the real axis. This is applied to the obstacle problem, partial balayage, quadrature domains and Hele-Shaw flow moving boundary problems, and we obtain sharp estimates of the curvature of free boundaries appearing in such problems.
Place, publisher, year, edition, pages
2003. Vol. 28, no 1, 123-142 p.
IdentifiersURN: urn:nbn:se:kth:diva-22468ISI: 000182609300009OAI: oai:DiVA.org:kth-22468DiVA: diva2:341166
QC 201005252010-08-102010-08-10Bibliographically approved