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.

Updated references, some notation clarified

References in corpus (4)

• Asymptotic expansions of solutions of the Yamabe equation and the ${\sigma }_k$-Yamabe equation near isolated singular points
• A ${\sigma }_2$ Penrose inequality for conformal asymptotically hyperbolic 4-discs
• On the ${\sigma }_k$-Nirenberg problem
• On a fully nonlinear Yamabe problem