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On perturbations of the fractional Yamabe problem. (English) Zbl 1371.35321

Summary: The fractional Yamabe problem, proposed by M. del Mar González and J. Qing [Anal. PDE 6, No. 7, 1535–1576 (2013; Zbl 1287.35039)], is a geometric question which concerns the existence of metrics with constant fractional scalar curvature. It extends the phenomena which were discovered in the classical Yamabe problem and the boundary Yamabe problem to the realm of nonlocal conformally invariant operators. We investigate a non-compactness property of the fractional Yamabe problem by constructing bubbling solutions to its small perturbations.

MSC:

35R11 Fractional partial differential equations
58J05 Elliptic equations on manifolds, general theory
35B33 Critical exponents in context of PDEs
35B44 Blow-up in context of PDEs
35R01 PDEs on manifolds

Citations:

Zbl 1287.35039
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References:

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