Liouville Type Equations with Singular Data¶and Their Applications to Periodic Multivortices¶for the Electroweak Theory

By Daniele Bartolucci, G. Tarantello. 2002

234 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/bf036064f14b2b09d09d4146773ecc7f79383b8b

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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.”
An Improved Geometric Inequality via Vanishing Moments, with Applications to Singular Liouville Equations (2012, methodology): “Notation and preliminaries This section contains some useful preliminary material, including elementary inequalities, some variants of the Moser-Trudinger inequality from [21], [34], [35], [53], and a compactness results from [11].”
Blow-up analysis of a Finsler–Liouville equation in two dimensions☆ (2012, methodology): “This approach was proposed by Bartolucci and Tarantello in [4], where they worked on singular Liouville equations.”
Profile of Blow-up Solutions to Mean Field Equations with Singular Data (2004, background): “…þ 2ð1þ aÞlog rk; ð3:6Þ then vk;1ðyÞ satisfies, Dvk;1ðyÞ þ Vk;1ðyÞevk;1ðyÞ ¼ oð1Þ for jyj 1 rk ; ð3:7Þ where Vk;1ðyÞ ¼ jyj2aV0ðrkyÞ: ð3:8Þ By Brezis and Merle’s result as extended in Bartolucci and Tarantello (2002), and in view of (3.5), there are two possibilities, either (i) vk;1ðyÞ is…”
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.”
Supercritical conformal metrics on surfaces with conical singularities (2011, background): “The difficulties are inherited by the lack of concentration-compactness-quantization results (in the same spirit of [2, 4, 29]) for solutions of (1.”
Weighted barycentric sets and singular Liouville equations on compact surfaces (2011, methodology): “While the recent papers [3] and in [35] (see also Corollary 6 in [6]) treated existence for positive α’s, more interesting for the physical applications, here we consider the case αj ∈ (−1, 0), which is geometrically more relevant.”