Details

Autor(en) / Beteiligte

• Allen, Mark
• Petrosyan, Arshak

Titel

A two-phase problem with a lower-dimensional free boundary

Ist Teil von

• Interfaces and free boundaries, 2012-01, Vol.14 (3), p.307-342

Ort / Verlag

Zuerich, Switzerland: European Mathematical Society Publishing House

Erscheinungsjahr

2012

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• For a bounded domain $D\subset \R^n$, we study minimizers of the energy functional \[ \int_{D}{|\nabla u|^2}\,dx + \int_{D \cap (\R^{n-1} \times \{0\} )}{\lambda^+ \chi_{ \{u > 0\} } + \lambda^- \chi_{ \{u 0\}\quad \text{and}\quad \Gamma^- = \partial \{u(\cdot, 0) < 0\} \] never touch. Moreover, using Alexandrov-type reflection technique, we can show that in dimension $n=3$ the free boundaries are $C^1$ regular on a dense subset.