Regularity for Fully Nonlinear Elliptic Equations with Neumann Boundary Data

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Regularity for Fully Nonlinear Elliptic Equations with Oblique Boundary Conditions (2017, methodology): “The proof for the A–B–P maximum principle has been motivated by [12], where the authors deal with the Neumann problems.”
Free boundary regularity for fully nonlinear non-homogeneous two-phase problems (2013, background): “.2 now follows from the corollary above and the (boundary) regularity theory for fully nonlinear uniformly elliptic equations (for the regularity result up to the boundary see [MW] or the Appendix in [MS].) We show below how to obtain (3.3), which concludes the proof of Theorem 3.2. Proof of (3.3). ”
Regularity for the nonlinear Signorini problem (2008, methodology): “1 in [10] we have that u (k) ∈ C(B1−δ/2).”
The Dirichlet problem for the convex envelope (2010, background): “This result is unusual for the following reason: loosely speaking, regularity results for elliptic PDEs (see [5] or [15] for more references) often fall into one of two categories.”
Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian (2007, methodology): “This implies that v is of class C2α in the x variable (see [5], or [15] to see an example where the method is only applied in the tangential direction).”