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

We study the boundary value problem for the — conformally invariant — super-Liouville functional $E\left(u,\psi \right)=\underset{M}{\int }\left\{\frac{1}{2}{|\nabla u|}^{2}+{K}_{g}u+〈\left(\mathrm{D}̸+{e}^{u}\right)\psi ,\psi 〉-{e}^{2u}\right\}\phantom{\rule{0.166667em}{0ex}}dz$ 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 $T\left(z\right)$, 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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