A free boundary problem related to thermal insulation: flat implies smooth View Full Text


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Article Info

DATE

2019-04

AUTHORS

Dennis Kriventsov

ABSTRACT

We study the regularity of the interface for a new free boundary problem introduced in Caffarelli and Kriventsov (A free boundary problem related to thermal insulation, 2015). We show that for minimizers of the functional F1(A,u)=∫A|∇u|2dLn+∫∂Au2+C¯Ln(A)over all pairs (A, u) of open sets A containing a fixed set Ω and functions u∈H1(A) which equal 1 on Ω, the boundary ∂A locally coincides with the union of the graphs of two C1,α functions near most points. Specifically, this happens at all points where the interface is trapped between two planes which are sufficiently close together. The proof combines ideas introduced by Ambrosio, Fusco, and Pallara for the Mumford–Shah functional with new arguments specific to the problem considered. More... »

PAGES

78

References to SciGraph publications

  • 1996. On the Regularity of the Edge Set of Mumford-Shah Minimizers in VARIATIONAL METHODS FOR DISCONTINUOUS STRUCTURES
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00526-019-1509-0

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    http://dx.doi.org/10.1007/s00526-019-1509-0

    DIMENSIONS

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