Gluing metrics with prescribed $Q$-curvature and different asymptotic behaviour in high dimension

DOI10.2422/2036-2145.201905_001zbMath1479.35467arXiv1804.09261OpenAlexW2997667196MaRDI QIDQ5161590

Ali Hyder, Luca Martinazzi

Publication date: 1 November 2021

Published in: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.09261

zbMATH Keywords

a priori estimatesblow-upradially symmetric solutions\(Q\)-curvature equation

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Blow-up in context of PDEs (35B44) Symmetries, invariants, etc. in context of PDEs (35B06) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (2)

Concentration phenomena for the fractional Q‐curvature equation in dimension 3 and fractional Poisson formulas ⋮ Concentration phenomena to a higher order Liouville equation

Cites Work

• Conformally Euclidean metrics on \(\mathbb{R}^n\) with arbitrary total Q-curvature
• Prescribing \(Q\)-curvature problem on \(S^n\)
• Classification of solutions to the higher order Liouville's equation on \({\mathbb{R}^{2m}}\)
• Concentration phenomena for a fourth-order equation with exponential growth: the radial case
• Singular limits in higher order Liouville-type equations
• Singular limits for the bi-Laplacian operator with exponential nonlinearity in \(\mathbb R^4\)
• Concentration-compactness phenomena in the higher order Liouville's equation
• Construction of singular limits for a semilinear elliptic equation in dimension 2
• A classification of solutions of a conformally invariant fourth order equation in \(\mathbb{R}^n\)
• On the existence of blowing-up solutions for a mean field equation
• Uniqueness and non-existence theorems for conformally invariant equations
• The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent
• A note on a class of higher order conformally covariant equations
• Critical points of the Moser-Trudinger functional on a disk
• Existence and asymptotics for solutions of a non-local Q-curvature equation in dimension three
• Structure of conformal metrics on \(\mathbb{R}^n\) with constant \(Q\)-curvature.
• Singular limits in Liouville-type equations
• The Moser-Trudinger inequality and its extremals on a disk via energy estimates
• Conformal metrics on \(\mathbb R^{2m}\) with constant \(Q\)-curvature and large volume
• Constant \(Q\)-curvature metrics in arbitrary dimension
• Singular limits for a 4-dimensional semilinear elliptic problem with exponential nonlinearity
• Concentration phenomena for Liouville's equation in dimension four
• QUANTIZATION FOR THE PRESCRIBED Q-CURVATURE EQUATION ON OPEN DOMAINS
• Asymptotics and Quantization for a Mean-Field Equation of Higher Order
• Asymptotic behavior of a fourth order mean field equation with Dirichlet boundary condition
• Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)e^uin two dimensions
• Large blow-up sets for the prescribed Q-curvature equation in the Euclidean space
• Asymptotic Profile for a Fourth Order PDE with Critical Exponential Growth in Dimension Four
• Quantization effects for a fourth-order equation of exponential growth in dimension $4$
• Compactness of solutions to some geometric fourth-order equations
• Bubbling phenomena for fourth-order four-dimensional PDEs with exponential growth
• Conformal metrics in \(\mathbb {R}^{2m}\) with constant \(Q\)-curvature and arbitrary volume

This page was built for publication: Gluing metrics with prescribed $Q$-curvature and different asymptotic behaviour in high dimension