We consider the non-local Liouville equation (−Δ)12u=hεeu−1inS1, corresponding to the prescription of the geodesic curvature on the circle. We build a family of solutions which blow up, when hε approaches a function h as ε → 0, at a critical point of the harmonic extension of h provided some generic assumptions are satisfied.
Battaglia, L., Medina, M., Pistoia, A. (2023). A blow-up phenomenon for a non-local Liouville-type equation. JOURNAL D'ANALYSE MATHEMATIQUE [10.1007/s11854-022-0260-1].
A blow-up phenomenon for a non-local Liouville-type equation
Battaglia L.
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2023-01-01
Abstract
We consider the non-local Liouville equation (−Δ)12u=hεeu−1inS1, corresponding to the prescription of the geodesic curvature on the circle. We build a family of solutions which blow up, when hε approaches a function h as ε → 0, at a critical point of the harmonic extension of h provided some generic assumptions are satisfied.File in questo prodotto:
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