We study the boundary value problem for the — conformally invariant — super-Liouville functional 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 , 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}, volume = {31}, year = {2014}, pages = {685-706}, doi = {10.1016/j.anihpc.2013.06.002}, mrnumber = {3249809}, zbl = {1319.30028}, language = {en}, url = {http://dml.mathdoc.fr/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, Tome 31 (2014) pp. 685-706. doi : 10.1016/j.anihpc.2013.06.002. http://gdmltest.u-ga.fr/item/AIHPC_2014__31_4_685_0/
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