Sharp estimates for solutions of multi‐bubbles in compact Riemann surfaces

By Chiun-Chuan Chen, Changshou Lin. 2002

323 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/9ec93078d985c059d2d4bc1bcb7da7a8d0dc090e

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In Applied Mathematics

In Computational Theory and Mathematics

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.”
Mean Field Equation of Liouville Type with Singular Data: Topological Degree (2015, methodology): “1, we will adopt the same strategy from [18, 19].”
Analytic aspects of the Toda system: II. Bubbling behavior and existence of solutions (2005, methodology): “Hence, again we can use the result in [6] for the Dirichlet boundary problem to get that the divergence of ṽ 1 implies that”
Classification of blowup limits for SU(3) singular Toda systems (2013, background): “MR 2000h:35045 Zbl 0961.35047 [Chen and Lin 2002] C.-C. Chen and C.-S. Lin, “Sharp estimates for solutions of multi-bubbles in compact Riemann surfaces”, Comm. Pure Appl.”
Profile of Blow-up Solutions to Mean Field Equations with Singular Data (2004, background): “Later, the second and third author in [10] could go further in this profile analysis to refine (1.”
Mean field equations, hyperelliptic curves and modular forms: I (2015, methodology): “ the heart inside the connection between (0.2) and (0.3) which we would like to explore. Suppose that fu kgis a sequence of bubbling solutions to (0.3) corresponding to r = r k. Then it was proved in [6] by PDE method that r k !8pn with n 2N, and the blow-up set fa 1, , angof fu kgmust satisfy (0.2)”
Compactness of solutions to some geometric fourth-order equations (2004, methodology): “lutions is used, reducing to problems on ﬂat domains like (11). This strategy has also been used in [20] to compute the total degree of the nonlinear equation, through the reﬁned blow-up estimates in [19] (see also [34]). Since every two-dimensional surface is locally conformally ﬂat, some of the an”
Existence of conformal metrics with constant Q-curvature (2004, methodology): “In this case non-compactness is expected, and the problem should require an asymptotic analysis as in [3], or a fine blow-up analysis as in [32], [19], [20].”
Weighted barycentric sets and singular Liouville equations on compact surfaces (2011, background): “This reduces all the problem to a blow-up analysis, which was in fact performed in [8] and later refined in [31], [30], [12] and [13].”
A deformation lemma with an application to a mean field equation (2007, background): “If furthermore T > 0, the refined blow-up analysis of Chen–Lin ([10, Theorem 6.2]) shows that actually the result of multiplicity hold on the full interval E (even at the possible value 8πN contained in E).”
Blowup Solutions of Some Nonlinear Elliptic Equations Involving Exponential Nonlinearities (2006, background): “Fourth, when it comes to estimate the error over the whole domain, we need an elegant lemma of Chen-Lin [5], which is included in the appendix.”
Profile of bubbling solutions to a Liouville system (2009, methodology): “The results of Li[21] and Bartolucci, Chen, Lin, Tarantello [3] have been improved by Chen and Lin [9] and Zhang [29,30] to a sharper form.”
Blow-up analysis of a Finsler–Liouville equation in two dimensions☆ (2012, background): “(2) have been intensively studied by many mathematicians, for there are many applications in geometric and physical problems, for example, in the problem of prescribing Gaussian curvature [9,12, 8], in the theory of the mean field equation [16,17,10,11,19,32] and in the Chern–Simons theory [38, 41,1”