W2,p- and W1,p-Estimates at the Boundary for Solutions of Fully Nonlinear, Uniformly Elliptic Equations

By N. Winter. 2009

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Regularity and uniqueness of the first eigenfunction for singular fully nonlinear operators (2009, background): “1) Observe first that since F̃ satisfies (F), by standard regularity results vδ ∈ W (Ω) for all p <∞ (see Evans [18], Caffarelli- Cabré [14] and Winter [34]).”
Principal eigenvalues and an anti-maximum principle for homogeneous fully nonlinear elliptic equations (2008, methodology): “ple in Ω for all suﬃciently large ρ. By replacing F with G−δ0, if necessary, we may assume F is proper. Select a continuous function h≤ 0, h≡ 0 with compact support in Ω. Standard results (see, e.g., [13, 14, 36]) imply the existence of a solution v∈ C1,α(Ω) of the Dirichlet problem ( F(D2v,Dv,v,x) ”