Free boundary regularity below the continuous threshold: 2-phase problems

✍ Scribed by Kenig, Carlos; Toro, Tatiana

• Book ID: 118740307
• Publisher: Walter de Gruyter GmbH & Co. KG
• Year: 2006
• Tongue: English
• Weight: 372 KB
• Volume: 2006
• Category: Article
• ISSN: 0075-4102
• DOI: 10.1515/CRELLE.2006.050

✦ Synopsis

In the present paper we continue our study of free boundary regularity problems for harmonic measure and Poisson kernels, below the continuous threshold. We focus our attention on 2-phase problems. We show that under the appropriate hypothesis for the free boundary data, if each phase is geometrically non-degenerate then the free boundary is regular. The main new point of this work is that no flatness condition on the free boundary is assumed a priori.