A unified approach of blow-up phenomena for two-dimensional singular Liouville systems

Luca Battaglia; Angela Pistoia

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arXiv · 1607.00427

A unified approach of blow-up phenomena for two-dimensional singular Liouville systems

Luca Battaglia·Angela Pistoia

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Abstract

We consider generic 2 x 2 singular Liouville systems on a smooth bounded domain in the plane having some symmetry with respect to the origin. We construct a family of solutions to which blow-up at the origin and whose local mass at the origin is a given quantity depending on the parameters of the system. We can get either finitely many possible blow-up values of the local mass or infinitely many. The blow-up values are produced using an explicit formula which involves Chebyshev polynomials.

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Luca Battaglia, Angela Pistoia. 2016-07-01. A unified approach of blow-up phenomena for two-dimensional singular Liouville systems. https://arxiv.org/abs/1607.00427

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