Solutions to a two-dimensional, Neumann free boundary problem. Issue 2 (25th January 2020)

• Record Type: Journal Article
• Authors: Gemmer, J. A.; Moon, G.; Raynor, S. G.
• Is Part Of: Applicable analysis. Volume 99:Issue 2(2020)
• Page Start: 214
• Page End: 231
• Publication Date: 2020-01-25
• Subjects: Free boundary problems -- elliptic regularity; 35R35 -- 35B65 -- 35J20 -- 35J60 -- 35J05 -- 35J25; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1489960
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: We explore regularity properties of solutions to a two-phase elliptic free boundary problem near a Neumann fixed boundary in two dimensions. Consider a function u, which is harmonic where it is not zero and satisfies a gradient jump condition weakly along the free boundary. Our main result is that u is Lipschitz continuous up to the Neumann fixed boundary. We also present a numerical exploration of the way in which the free and fixed boundaries interact.