The two-phase membrane problem¿An intersection-comparison approach to the regularity at branch points

• Autores: Henrik Shahgholian, Georg S. Weiss
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 205, Nº 2, 2006, págs. 487-503
• Idioma: inglés
• DOI: 10.1016/j.aim.2005.07.015
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• Resumen

  • For the two-phase membrane problemwhere and we prove in two dimensions that the free boundary is in a neighborhood of each ?branch point? the union of two -graphs. We also obtain a stability result with respect to perturbations of the boundary data. Our analysis uses an intersection-comparison approach based on the Aleksandrov reflection.

    In higher dimensions we show that the free boundary has finite -dimensional Hausdorff measure.