Interior W2,δ type estimates for degenerate fully nonlinear elliptic equations with Ln data ☆

초록

We establish interior W2,delta type estimates for a class of degenerate fully nonlinear elliptic equations with Lndata. The main idea of our approach is to slide C1,alpha cones, instead of paraboloids, vertically to touch the solution, and estimate the contact set in terms of the measure of the vertex set. This shows that the solution has tangent C1,alpha cones almost everywhere, which leads to the desired Hessian estimates. Accordingly, we are able to develop a kind of counterpart to the estimates for divergent structure quasilinear elliptic problems, as discussed in [6,16]. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

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