Bubbling phenomena for fourth-order four-dimensional PDEs with exponential growth
From MaRDI portal
Publication:5713212
DOI10.1090/S0002-9939-05-08330-9zbMath1083.58018MaRDI QIDQ5713212
Olivier Druet, Frédéric Robert
Publication date: 12 December 2005
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Variational principles in infinite-dimensional spaces (58E30) Elliptic equations on manifolds, general theory (58J05) Variational methods for higher-order elliptic equations (35J35)
Related Items (33)
Prescribing \(Q\)-curvature problem on \(S^n\) ⋮ Concentration phenomena for a fourth-order equation with exponential growth: the radial case ⋮ Classification and a priori estimates for the singular prescribing \(Q\)-curvature equation on 4-manifold ⋮ The nonlocal Liouville-type equation in \(\mathbb {R}\) and conformal immersions of the disk with boundary singularities ⋮ ``Large conformal metrics of prescribed \(Q\)-curvature in the negative case ⋮ Multibubble analysis on \(N\)-Laplace equation in \({\mathbb{R}^N}\) ⋮ Topological methods for the resonant \(Q\)-curvature problem in arbitrary even dimension ⋮ Compactness properties for geometric fourth order elliptic equations with application to the \(Q\)-curvature flow ⋮ Existence and compactness of conformal metrics on the plane with unbounded and sign-changing Gaussian curvature ⋮ Bubbling solutions of fourth order mean field equations on \(\mathbb{S}^4\) ⋮ Optimal control for the Paneitz obstacle problem ⋮ The prescribed \(Q\)-curvature flow for arbitrary even dimension in a critical case ⋮ Critical metrics for log-determinant functionals in conformal geometry ⋮ Topological degree for solutions of fourth order mean field equations ⋮ The \(Q\)-curvature on a 4-dimensional Riemannian manifold \((M,g)\) with \(\int_M QdV_g = 8\pi^2\) ⋮ Conformal metrics on \(\mathbb R^{2m}\) with constant \(Q\)-curvature and large volume ⋮ Compactness of conformal metrics with constant \(Q\)-curvature. I ⋮ New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces ⋮ Constant \(Q\)-curvature metrics in arbitrary dimension ⋮ An estimate on the blowing-up solutions of a fourth-order equation ⋮ Singular limits for the bi-Laplacian operator with exponential nonlinearity in \(\mathbb R^4\) ⋮ Gluing metrics with prescribed $Q$-curvature and different asymptotic behaviour in high dimension ⋮ Existence and multiplicity results for a fourth order mean field equation ⋮ Multibumps analysis in dimension 2: quantification of blow-up levels ⋮ Existence and asymptotics for solutions of a non-local Q-curvature equation in dimension three ⋮ Concentration phenomena for Liouville's equation in dimension four ⋮ Generic multiplicity for a scalar field equation on compact surfaces ⋮ Existence of solutions to a higher dimensional mean-field equation on manifolds ⋮ Concentration phenomena for the fractional Q‐curvature equation in dimension 3 and fractional Poisson formulas ⋮ Concentration-compactness phenomena in the higher order Liouville's equation ⋮ The profile of bubbling solutions of a class of fourth order geometric equations on 4-manifolds ⋮ Concentration phenomena to a higher order Liouville equation ⋮ A mean field type flow. I: compactness of solutions to a perturbed mean field type equation
Cites Work
- A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds (Summary)
- A classification of solutions of a conformally invariant fourth order equation in \(\mathbb{R}^n\)
- From one bubble to several bubbles: the low-dimensional case.
- Blow-up examples for second order elliptic PDEs of critical Sobolev growth
- Asymptotic Profile for a Fourth Order PDE with Critical Exponential Growth in Dimension Four
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Bubbling phenomena for fourth-order four-dimensional PDEs with exponential growth