论文标题
Riemannian域上半线性PDE的解决方案的对称性
Symmetry of solutions of semilinear PDEs on Riemannian domains
论文作者
论文摘要
本文介绍了对称现象，用于涉及Riemannian领域半线性PDE的DIRICHLET问题的解决方案。我们将提出一个相当普遍的框架，可以在其中提出对称问题，并提供一些证据，表明该框架是完全自然的，通过指出一些稳定解决方案的结果。从一开始就插入了具有密度和相应加权拉普拉斯的歧管的情况。
This paper deals with symmetry phenomena for solutions of the Dirichlet problem involving semilinear PDEs on Riemannian domains. We shall present a rather general framework where the symmetry problem can be formulated and provide some evidence that this framework is completely natural by pointing out some results for stable solutions. The case of manifolds with density, and corresponding weighted Laplacians, is inserted in the picture from the very beginning.
