The structure of the free boundary in the fully nonlinear thin obstacle problem
2017; Elsevier BV; Volume: 316; Linguagem: Inglês
10.1016/j.aim.2017.06.032
ISSN1090-2082
AutoresXavier Ros‐Oton, Joaquim Serra,
Tópico(s)Geometric Analysis and Curvature Flows
ResumoWe study the regularity of the free boundary in the fully nonlinear thin obstacle problem. Our main result establishes that the free boundary is C1 near any regular point. This extends to the fully nonlinear setting the celebrated result of Athanasopoulos–Caffarelli–Salsa [1]. The proofs we present here are completely independent from those in [1], and do not rely on any monotonicity formula. Furthermore, an interesting and novel feature of our proofs is that we establish the regularity of the free boundary without classifying blow-ups, a priori they could be non-homogeneous and/or non-unique. We do not classify blow-ups but only prove that they are 1D on {xn=0}.
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