Journal
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
Volume 17, Issue 6, Pages 1293-1326Publisher
EUROPEAN MATHEMATICAL SOC
DOI: 10.4171/JEMS/531
Keywords
Energy minimizers; one-phase free boundary problem; monotonicity formula
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Funding
- NSF grant [DMS-1301535, DMS-1200701]
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We study regularity properties of the free boundary for the thin one-phase problem which consists in minimizing the energy functional E(u, Omega) = integral(Omega) vertical bar del u vertical bar(2) dX + H-n ({u > 0} boolean AND {x(n+1) = 0}), Omega subset of R-,(n+1) among all functions u >= 0 which are fixed on partial derivative Omega.
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