Singular Solutions of Fractional Order Conformal Laplacians

By Maria Mar González, Rafe Mazzeo, Yannick Sire. 2009

115 citations recorded by the source corpus.

We investigate the singular sets of solutions of a natural family of conformally covariant pseudodifferential elliptic operators of fractional order, with the goal of developing generalizations of some well-known properties of solutions of the singular Yamabe problem.

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

View Paper: https://www.semanticscholar.org/paper/2decb1e70d2511e8e97bf56bf94866d9c2af7bd1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Some constructions for the fractional Laplacian on noncompact manifolds (2012, background): “In [30] singular fractional Yamabe problems were considered in the particular case that M = Sn\Λ, where the singular set Λ is a smooth k-dimensional submanifold and gM a complete metric with controlled growth near the singular set.”
A fractional Yamabe flow and some applications (2011, background): “have been several work on these conformally invariant equations of fractional order and prescribing σ-curvatures problem (fractional Yamabe problem and fractional Nirenberg problem), see, e.g., [68], [39], [40], [51] and [52]. In this paper we study some ﬂow of this fractional order curvature Rg σ a”
On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions (2011, background): “Fractional Yamabe problems about finding constant σ -curvatures on the conformal infinity of given asymptotically hyperbolic manifolds have been studied by González, Mazzeo and Sire [54], González and Qing [55] and Qing and Raske [87].”
Fractional Laplacian in conformal geometry (2010, background): “On one hand, there are extensive works that study properties of fractional Laplacian operators as non-local operators together with applications to free-boundary value problems and non-local minimal surfaces—by Caffarelli and Silvestre [6], and many others (see the related articles [5,7,4,9]); on th”
The Nirenberg problem and its generalizations: a unified approach (2014, background): “[37], González and Qing [38]; fractional Yamabe flows and weighted trace inequalities by Jin and Xiong [53,54]; analysis of local solutions of (1.”
Local Analysis of Solutions of Fractional Semi-Linear Elliptic Equations with Isolated Singularities (2013, background): “A s imilar upper bound in ( 3) was obtained in [9] under additional assumptions that the equations are globa lly s tisfied on thewholespace and the conformal metric is complete.”
SHARP HARDY-LITTLEWOOD-SOBOLEV INEQUALITY ON THE UPPER HALF SPACE (2013, result): “]. See also our recent work [14] for equations with negative exponent. Our results are closely related to the study of fractional Lapalacian operator in the whole space [8], fractional Yamabe problem [9, 22, 23, 25, 33, 34], fractional 6 prescribing curvature problem on Sn [31, 32], and to the study”