Boundary pointwise C1, and C2, regularity for fully nonlinear elliptic equations

${W}^{2,p}$ Estimates for Elliptic Equations on $C^{1,α}$ Domains

“…The next lemma concerns pointwise boundary C 1,α estimates and we refer to Theorem 1.6 in [8] for its proof. Lemma 3.2.…”

“…From Theorem 5.1, we see again that by Whitney decomposition, local boundary W 2,p estimate follows from interior W 2,p estimate and boundary C 1,α estimate which are assumed. As for interior W 2,p estimate, we refer to [1] and Theorem 7.1 in [2]; as for boundary C 1,α estimate, we refer to [8] and [10].…”

${{W}^{2,δ}}$ Estimates for Solution Sets of Fully Nonlinear Elliptic inequalities on ${C^{1,α}}$ Domains

“…Based on Lemma 3.2, Lian and Zhang [10] proved the following lemma concerning pointwise boundary C 1,α estimates for u ∈ S(λ, Λ, f ) on C 1,α domains for 0 < α < ᾱ by compactness method. Lemma 3.3.…”

Boundary pointwise regularity and applications to the regularity of free boundaries

“…It can be tracked at least to the work of Caffarelli [3] for the interior pointwise regularity of fully nonlinear elliptic equations. Various pointwise regularity have been developed by many researchers since then, such as boundary regularity ([12], [20]), regularity for equations with lower terms ( [19], [20], [11], [15], [21]), regularity for parabolic equations ( [22,23,24]) and regularity for the Monge-Ampère equation ( [18]) etc.…”