Partial Regularity for Harmonic Maps into Spheres at a Singular or Degenerate Free Boundary

DOI10.1007/S12220-021-00788-WzbMATH Open1521.58006arXiv2010.07688WikidataQ114221027 ScholiaQ114221027MaRDI QIDQ6351390

Roger Moser, James W. Roberts

Publication date: 15 October 2020

Abstract: We prove partial regularity of weakly stationary harmonic maps with (partially) free boundary data on manifolds where the domain metric may degenerate or become singular along the free boundary at the rate $d^{a}lpha$ for the distance function $d$ from the boundary.

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Degenerate elliptic equations (35J70) Harmonic maps, etc. (58E20) Free boundary problems for PDEs (35R35)

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