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

Henrik Shahgholian, Georg S. Weiss

• 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.