On conformally invariant equations on \(R^n\)-II. Exponential invariance

DOI10.1016/j.na.2012.04.036zbMath1250.35068OpenAlexW2071326539WikidataQ126011436 ScholiaQ126011436MaRDI QIDQ435103

Paolo Mastrolia, Yan-yan Li, Dario Daniele Monticelli

Publication date: 16 July 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2012.04.036

zbMATH Keywords

Schouten tensorconformally invariant operatorsexponential invariancefully nonlinear higher order equations

Mathematics Subject Classification ID

Nonlinear higher-order PDEs (35G20) Invariance and symmetry properties for PDEs on manifolds (58J70) Geometric theory, characteristics, transformations in context of PDEs (35A30) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items

On conformally invariant equations on \(\mathbf R^n\), Classification theorems for solutions of higher order boundary conformally invariant problems. I., Concentration of solutions for the fractional Nirenberg problem, On conformally invariant equations on \(R^n\)-II. Exponential invariance, On the relation between conformally invariant operators and some geometric tensors, Peak solutions for the fractional Nirenberg problem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On conformally invariant equations on \(R^n\)-II. Exponential invariance
• Asymptotic behavior of solutions to the \(\sigma_{k}\)-Yamabe equation near isolated singularities
• Fractional Laplacian in conformal geometry
• On fully nonlinear CR invariant equations on the Heisenberg group
• \(Q\)-curvature and Poincaré metrics
• Higher symmetries of the Laplacian
• Singular sets of a class of locally conformally flat manifolds
• Removability of singularities for a class of fully nonlinear elliptic equations
• Variational status of a class of fully nonlinear curvature prescription problems
• A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds (Summary)
• Degenerate conformally invariant fully nonlinear elliptic equations
• On the decomposition of global conformal invariants. I.
• On the \(\sigma_2\)-scalar curvature
• Conformally invariant differential operators on Minkowski space and their curved analogues
• Conformally invariant powers of the Laplacian, \(Q\)-curvature, and tractor calculus
• Scattering matrix in conformal geometry
• Conformally covariant pseudo-differential operators
• A fully nonlinear equation on four-manifolds with positive scalar curvature.
• An a priori estimate for a fully nonlinear equation on four-manifolds.
• Estimates and existence results for some fully nonlinear elliptic equations on Riemannian manifolds
• An equation of Monge-Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature
• Geometric inequalities on locally conformally flat manifolds
• Conformal geometry, contact geometry, and the calculus of variations
• A Kazdan-Warner type identity for the \(\sigma_{k}\) curvature
• Existence of conformal metrics with constant \(Q\)-curvature
• The Yamabe problem for higher order curvatures
• Prescribing symmetric functions of the eigenvalues of the Ricci tensor
• Conformally invariant fully nonlinear elliptic equations and isolated singularities
• On some conformally invariant fully nonlinear equations. II: Liouville, Harnack and Yamabe
• Classification of singular radial solutions to the \(\sigma_k\) Yamabe equation on annular domains
• Conformally Invariant Powers of the Laplacian, I: Existence
• On a fully nonlinear Yamabe problem
• A Class of Variational Functionals in Conformal Geometry
• Regularity of a Fourth Order Nonlinear PDE with Critical Exponent
• On some conformally invariant fully nonlinear equations
• Local gradient estimates of solutions to some conformally invariant fully nonlinear equations