论文标题
奇异定理在渐近抗DE保姆空间上的传播的概括
A generalization of the propagation of singularities theorem on asymptotically anti-de Sitter spacetimes
论文作者
论文摘要
在最近的一篇论文中，O. Gannot和M. Wrochna在渐近的反DE保姆时空上考虑了klein-gordon方程，但受罗宾边界条件的约束，特别是奇异定理的传播。在这项工作中，我们概括了他们的结果，考虑到通过合适顺序的伪差操作员在共形边界上实现的更一般的边界条件类别。使用$ b $ calculus和扭曲的Sobolev空间的技术，我们也证明了沿着广义破碎的双分裂分数的奇异定理的传播，这突出了由于编码边界条件的伪数操作员而可能存在贡献。
In a recent paper O. Gannot and M. Wrochna considered the Klein-Gordon equation on an asymptotically anti-de Sitter spacetime subject to Robin boundary conditions, proving in particular a propagation of singularity theorem. In this work we generalize their result considering a more general class of boundary conditions implemented on the conformal boundary via pseudodifferential operators of suitable order. Using techniques proper of $b$-calculus and of twisted Sobolev spaces, we prove also for the case in hand a propagation of singularity theorem along generalized broken bicharacteristics, highlighting the potential presence of a contribution due to the pseudodifferential operator encoding the boundary condition.
