Open AccessA two-phase problem with a lower-dimensional free boundary
Author(s) -
M. Allen,
Arshak Petrosyan
Publication year - 2012
Publication title -
interfaces and free boundaries mathematical analysis computation and applications
Language(s) - English
Resource type - Journals
eISSN - 1463-9971
pISSN - 1463-9963
DOI - 10.4171/ifb/283
Subject(s) - phase (matter) , boundary (topology) , free boundary problem , geometry , mathematics , computer science , mathematical analysis , physics , quantum mechanics
For a bounded domain D ⊂ Rn, we study minimizers of the energy functional ∫ D |∇u| dx+ ∫ D∩(Rn−1×{0}) λχ{u>0} + λ χ{u 0} and Γ− = ∂{u(·, 0) < 0} never touch. Moreover, using Alexandrov-type reflection technique, we can show that in dimension n = 3 the free boundaries are C1 regular on a dense subset.
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