The Liouville Equation with Singular Data: A Concentration-Compactness Principle via a Local Representation Formula☆

By Daniele Bartolucci, G. Tarantello. 2002

63 citations recorded by the source corpus.

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Citations in the corpus

Compactness of solutions to the Yamabe problem (2004, unknown): “Analogous results, extensions, as well as different proofs of (12) can be found in [87], [90], [81], [22], [21], [74], [34], [33], [68], [16], [ 17 ], [36], [69], [64], [14], [78], [37], [65], [15], [88], [89], and others.”
Weighted barycentric sets and singular Liouville equations on compact surfaces (2011, background): “With respect to equation (2), much of the existing literature concerns asymptotic analysis or compactness of solutions (see for instance [6], [7], [14], [38], [41]), while relatively few results are available about existence.”
Classification of blowup limits for SU(3) singular Toda systems (2013, methodology): “MR 2003h:35063 Zbl 1247.35032 [Bartolucci and Tarantello 2002b] D. Bartolucci and G. Tarantello, “Liouville type equations with singular data and their applications to periodic multivortices for the electroweak theory”, Comm. Math.”
Mean Field Equation of Liouville Type with Singular Data: Topological Degree (2015, background): “It is well-known that if … †, where † WD ˚ 8m C†q2A8 .1C ˛.q// j A fq1; : : : ; qN g; m 2 N C [ f0g n f0g; MEAN FIELD EQUATION: TOPOLOGICAL DEGREE 889 then the a priori bound holds; i.e., there exists a constant C such that for all solutions of (1.4), ju.x/j C 8x 2M: The study of a priori bounds beg”
Singular limits in Liouville-type equations (2005, background): “In case they exist, they provide an extra contribution 8π(1 + α) to the above limit, see [3, 31].”
Some existence results for the Toda system on closed surfaces (2007, background): “arises in the study of mean field limit of point vortices of Euler flows, spherical Onsager vortex theory and condensates in some Chern-Simons-Higgs models, see for example the papers [ 3 ], [4], [7], [8], [9], [10], [12], [20], [30] and the references therein.”