Concentration–compactness phenomena in the higher order Liouville's equation☆
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TLDR
In this paper, the authors investigated different concentration-compactness and blow-up phenomena related to the Q-curvature in arbitrary even dimension and showed that on a locally conformally flat manifold of non-positive Euler characteristic, one always has compactness.About:
This article is published in Journal of Functional Analysis.The article was published on 2009-06-01 and is currently open access. It has received 56 citations till now. The article focuses on the topics: Closed manifold & Conformally flat manifold.read more
Citations
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Supercritical conformal metrics on surfaces with conical singularities
TL;DR: In this paper, the authors studied the problem of prescribing the Gaussian curvature on surfaces with conical singularities in supercritical regimes using a Morse-theoretical approach.
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Existence and asymptotics for solutions of a non-local Q-curvature equation in dimension three
TL;DR: In this article, Chen et al. studied conformal metrics of the form (g_u=e^{2u}|dx|^2$$�, which have constant curvature and finite volume.
Journal ArticleDOI
Blow-up analysis of a nonlocal Liouville-type equation
TL;DR: In this article, a blow-up and quantization analysis of the following nonlocal Liouville-type equation is performed, where the curvature equation is interpreted as a curve in conformal parametrization.
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Blow-up analysis of a nonlocal Liouville-type equation
TL;DR: In this article, an equivalence between the Nirenberg problem on the circle and the boundary of holomorphic immersions of the dis ki nto the plane has been established, and the following nonlocal Liouville-type equation is studied.
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“Large” conformal metrics of prescribed Gauss curvature on surfaces of higher genus
TL;DR: In this article, a more refined mountain pass technique was used to obtain additional estimates for the large solutions u that allow to characterize their bubblebling behavior as λ ↓ 0, where uλ is a relative minimizer of the associated variational integral.
References
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Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
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Elliptic Partial Differential Equations of Second Order
David Gilbarg,Neil S. Trudinger +1 more
TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.
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Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
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Interpolation of operators
C. Bennett,M Sharpley +1 more
TL;DR: In this article, the classical interpolation theorem is extended to the Banach Function Spaces, and the K-Method is used to find a Banach function space with a constant number of operators.
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