Concentration phenomena for Liouville's equation in dimension four

DOI10.4171/JEMS/44zbMath1387.35198OpenAlexW1975315709MaRDI QIDQ2502546

Adimurthi, Frédéric Robert, Michael Struwe

Publication date: 13 September 2006

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/jems/44

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Nonlinear elliptic equations (35J60)

Related Items (32)

Normal conformal metrics on \(\mathbb{R}^4\) with singular \(Q\)-curvature having power-like growth ⋮ Classification of solutions to the higher order Liouville's equation on \({\mathbb{R}^{2m}}\) ⋮ Quantization for a fourth order equation with critical exponential growth ⋮ The convergence of nonnegative solutions for the family of problems −Δ_pu=λe^uasp→∞ ⋮ Local and Nonlocal Singular Liouville Equations in Euclidean Spaces ⋮ 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 ⋮ Classification of solutions to a system of \(n^{\mathrm{th}}\) order equations on \(\mathbb{R}^n\) ⋮ ``Large conformal metrics of prescribed \(Q\)-curvature in the negative case ⋮ Large blow-up sets for the prescribed Q-curvature equation in the Euclidean space ⋮ Bubbling solutions of fourth order mean field equations on \(\mathbb{S}^4\) ⋮ Asymptotic behavior of least energy nodal solutions for biharmonic Lane-Emden problems in dimension four ⋮ 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 ⋮ Quantization for an elliptic equation of order \(2m\) with critical exponential non-linearity ⋮ An estimate on the blowing-up solutions of a fourth-order equation ⋮ Uniform bounds for higher-order semilinear problems in conformal dimension ⋮ Singular limits for the bi-Laplacian operator with exponential nonlinearity in \(\mathbb R^4\) ⋮ Priori estimates and asymptotic properties of solutions for some fractional order elliptic equations ⋮ Gluing metrics with prescribed $Q$-curvature and different asymptotic behaviour in high dimension ⋮ Conformally Euclidean metrics on \(\mathbb{R}^n\) with arbitrary total Q-curvature ⋮ Existence and multiplicity results for a fourth order mean field equation ⋮ 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 ⋮ The heat flow with a critical exponential nonlinearity ⋮ Theoretical developments in the study of partial differential equations ⋮ 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 ⋮ Asymptotic behavior of solutions of a biharmonic Dirichlet problem with large exponents

Cites Work

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