Regularity of Free Boundaries in Obstacle-type Problems

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An epiperimetric inequality approach to the regularity of the free boundary in the Signorini problem with variable coefficients (2015, background): “ Γ3/2(v), and B′ η0 ∩Λ(v) = B ′ η0 ∩{xn−1 ≤ g(x1,...,xn−2)} for g∈ C1,β(Rn−2) with a universal exponent β∈ (0,1). Thisresult is known and well-understood in the case L= ∆, see [ACS08] or Chapter 9 in [PSU12]. However, the existing proofs are based on diﬀerentiating the equation for vin tangential di”
Regularity Theory for Elliptic PDE (2022, methodology): “that are not covered in [CC95]; and we also include a detailed study of the obstacle problem, often left to more specialized textbooks such as [Fri88] or [PSU12].”
Higher regularity of the free boundary in the elliptic Signorini problem (2014, background): “9 in [21], we must have the form u0 = C0 Re(x′ · e′ + ixn) for some C0 > 0 and a tangential unit vector e′ ∈ ∂B′ 1.”