Local pointwise second derivative estimates for strong solutions to the ${\sigma }_k$-Yamabe equation on Euclidean domains

Abstract

We prove local pointwise second derivative estimates for positive $W^{2,p}$ solutions to the ${\sigma }_k$-Yamabe equation on Euclidean domains, addressing both the positive and negative cases. Generalisations for augmented Hessian equations are also considered.

arXiv commentUpdated references, some notation clarified

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