TY - JOUR
T1 - Optimal regularity for the thin obstacle problem with C0 , α coefficients
AU - Rüland, Angkana
AU - Shi, Wenhui
PY - 2017/10/1
Y1 - 2017/10/1
N2 - In this article we study solutions to the (interior) thin obstacle problem under low regularity assumptions on the coefficients, the obstacle and the underlying manifold. Combining the linearization method of Andersson (Invent Math 204(1):1–82, 2016. doi:10.1007/s00222-015-0608-6) and the epiperimetric inequality from Focardi and Spadaro (Adv Differ Equ 21(1–2):153–200, 2016), Garofalo, Petrosyan and Smit Vega Garcia (J Math Pures Appl 105(6):745–787, 2016. doi:10.1016/j.matpur.2015.11.013), we prove the optimal C1 , min { α , 1 / 2 } regularity of solutions in the presence of C0 , α coefficients ai j and C1 , α obstacles ϕ. Moreover we investigate the regularity of the regular free boundary and show that it has the structure of a C1 , γ manifold for some γ∈ (0 , 1).
AB - In this article we study solutions to the (interior) thin obstacle problem under low regularity assumptions on the coefficients, the obstacle and the underlying manifold. Combining the linearization method of Andersson (Invent Math 204(1):1–82, 2016. doi:10.1007/s00222-015-0608-6) and the epiperimetric inequality from Focardi and Spadaro (Adv Differ Equ 21(1–2):153–200, 2016), Garofalo, Petrosyan and Smit Vega Garcia (J Math Pures Appl 105(6):745–787, 2016. doi:10.1016/j.matpur.2015.11.013), we prove the optimal C1 , min { α , 1 / 2 } regularity of solutions in the presence of C0 , α coefficients ai j and C1 , α obstacles ϕ. Moreover we investigate the regularity of the regular free boundary and show that it has the structure of a C1 , γ manifold for some γ∈ (0 , 1).
KW - 35R35
UR - http://www.scopus.com/inward/record.url?scp=85028347949&partnerID=8YFLogxK
U2 - 10.1007/s00526-017-1230-9
DO - 10.1007/s00526-017-1230-9
M3 - Article
AN - SCOPUS:85028347949
VL - 56
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
SN - 0944-2669
IS - 5
M1 - 129
ER -