Local pointwise second derivative estimates for strong solutions to the $$\sigma _k$$-Yamabe equation on Euclidean domains
Copyright policy )Local pointwise second derivative estimates for strong solutions to the $$\sigma _k$$-Yamabe equation on Euclidean domains
AbstractWe prove local pointwise second derivative estimates for positive $$W^{2,p}$$ W 2 , p solutions to the $$\sigma _k$$ σ k -Yamabe equation on Euclidean domains, addressing both the positive and negative cases. Generalisations for augmented Hessian equations are also considered.
Mathematics - Differential Geometry, Smoothness and regularity of solutions to PDEs, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Strong solutions to PDEs, Nonlinear elliptic equations, 35B65 (Primary) 35D35, 35J15, 35J60, 53C21 (Secondary), A priori estimates in context of PDEs, Second-order elliptic equations, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), FOS: Mathematics, augmented Hessian equations, Analysis of PDEs (math.AP)
Mathematics - Differential Geometry, Smoothness and regularity of solutions to PDEs, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Strong solutions to PDEs, Nonlinear elliptic equations, 35B65 (Primary) 35D35, 35J15, 35J60, 53C21 (Secondary), A priori estimates in context of PDEs, Second-order elliptic equations, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), FOS: Mathematics, augmented Hessian equations, Analysis of PDEs (math.AP)
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