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• W1963977425 abstract "For a bounded domain $Dsubset R^n$, we study minimizers of the energy functional $$ int_{D}{|nabla u|^2},dx + int_{D cap (R^{n-1} times {0} )}{lambda^+ chi_{ {u > 0} } + lambda^- chi_{ {u<0} }}, dH^{n-1}, $$ without any sign restriction on the function $u$. One of the main result states that the free boundaries $$ Gamma^+ = partial {u(cdot,0) > 0}quad text{and}quad Gamma^- = partial {u(cdot, 0) < 0} $$ 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." @default.
• W1963977425 created "2016-06-24" @default.
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• W1963977425 date "2012-01-01" @default.
• W1963977425 modified "2023-10-16" @default.
• W1963977425 title "A two-phase problem with a lower-dimensional free boundary" @default.
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• W1963977425 doi "https://doi.org/10.4171/ifb/283" @default.
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