On the Yamabe problem and the scalar curvature problems under boundary conditions

By A. Ambrosetti, Yanyan Li, A. Malchiodi. 2002

79 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8044de46352682223b9028068ffe50862f473753

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Citations in the corpus

Compactness of solutions to the Yamabe problem (2004, unknown): “There have been many works on the existence of solutions to the Yamabe problem, the Nirenberg problem, and the Yamabe problem on manifolds with boundary, see for instance [76], [62], [42], [43], [61], [50], [29], [30], [39], [38], [55], [59], [31], [46], [47], [19], [28], [48], [7], [8], [40], [2], ”
Compactness results in conformal deformations of Riemannian metrics on manifolds with boundaries (2001, background): “[5], and existence results in many cases were obtained by Escobar, see [7, 9]. Related problems regarding conformal deformations of Riemannian metrics on manifolds with boundaries have been studied in [ 1 , 4, 6, 8, 12, 13, 14, 18, 19, 23, 25]; see also the references therein.”
Estimates and existence results for a fully nonlinear Yamabe problem on manifolds with boundary (2006, background): “37 References [1] A. Ambrosetti, Y. Y. Li and A. Malchiodi, On the Yamabe problem and the scalar curvature problems under boundary conditions, Math.”
An existence theorem of conformal scalar-flat metrics on manifolds with boundary (2009, background): “Other works concerning conformal deformation on manifolds with boundary include [Ahmedou 2003; Ambrosetti et al. 2002; Ben Ayed et al. 2005; Brendle 2002; Djadli et al. 2003; 2004; Escobar 1992b; 1996a; Escobar and Garcia 2004; Felli and Ould Ahmedou 2003; 2005; Han and Li 1999; 2000] We will now di”
Bifurcation results for a fractional elliptic equation with critical exponent in R^n (2014, background): “a huge literature concerning the search of solutions for this kind of perturbative problems in the classical case, i.e. when s= 1 and the fractional Laplacianboils down to the classicalLaplacian, see [1, 2, 3, 4, 5, 8, 10, 14, 15, 31, 32]. In particular, Theorems 1.1 and 1.2 here can be seen as the ”
Fractional elliptic problems with critical growth in the whole of $\R^n$ (2015, background): “In the classical case, that is when s = 1 and the fractional Laplacian boils down to the classical Laplacian, there is an intense literature regarding this type of problems, see [1, 2, 3, 4, 5, 6, 9, 13, 18, 22, 24, 38, 39], and references therein.”
On some conformally invariant fully nonlinear equations, II. Liouville, Harnack and Yamabe (2005, background): “The problem has been studied by many authors, see, e.g., Cherrier ([17]), Escobar ([19], [20], [21] and [22]), Han and Li ([39] and [40]), Ambrosetti, Malchiodi and Li ([ 1 ]), Brendle ([5]), and the references therein.”