A free boundary problem related to thermal insulation. Issue 7 (2nd July 2016)

• Record Type: Journal Article
• Authors: Caffarelli, Luis A.; Kriventsov, Dennis
• Is Part Of: Communications in partial differential equations. Volume 41:Issue 7(2016)
• Page Start: 1149
• Page End: 1182
• Publication Date: 2016-07-02
• Subjects: Free boundary -- free discontinuity -- insulation -- Robin; 35R35; Differential equations, Partial -- Periodicals; 515.353
• DOI: 10.1080/03605302.2016.1199038
• Languages: English
• ISSNs: 0360-5302

Abstract

ABSTRACT: We study a free boundary problem arising from the theory of thermal insulation. The outstanding feature of this set optimization problem is that the boundary of the set being optimized is not a level surface of a harmonic function, but rather a hypersurface along which a harmonic function satisfies a Robin condition. We show that minimal sets exist, satisfy uniform density estimates, and, under some geometric conditions, have "locally flat" boundaries.