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.
Cite this article
Jürgen Jost, Guofang Wang, Chunqin Zhou, Miaomiao Zhu, The boundary value problem for the super-Liouville equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 4, pp. 685–706DOI 10.1016/J.ANIHPC.2013.06.002