The boundary value problem for the super-Liouville equation
Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 4, p. 685-706
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We study the boundary value problem for the — conformally invariant — super-Liouville functional E(u,ψ)= M{1 2|u| 2 +K g u+(D̸+e u )ψ,ψ-e 2u }dz that couples a function u and a spinor ψ on a Riemann surface. The boundary condition that we identify (motivated by quantum field theory) couples a Neumann condition for u with a chirality condition for ψ. Associated to any solution of the super-Liouville system is a holomorphic quadratic differential T(z), and when our boundary condition is satisfied, T becomes real on the boundary. We provide a complete regularity and blow-up analysis for solutions of this boundary value problem.

@article{AIHPC_2014__31_4_685_0,
     author = {Jost, J\"urgen and Wang, Guofang and Zhou, Chunqin and Zhu, Miaomiao},
     title = {The boundary value problem for the super-Liouville equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {31},
     number = {4},
     year = {2014},
     pages = {685-706},
     doi = {10.1016/j.anihpc.2013.06.002},
     zbl = {1319.30028},
     mrnumber = {3249809},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2014__31_4_685_0}
}
Jost, Jürgen; Wang, Guofang; Zhou, Chunqin; Zhu, Miaomiao. The boundary value problem for the super-Liouville equation. Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 4, pp. 685-706. doi : 10.1016/j.anihpc.2013.06.002. http://www.numdam.org/item/AIHPC_2014__31_4_685_0/

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