当前位置: X-MOL 学术C. R. Math. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Analysis and boundary value problems on singular domains: An approach via bounded geometry
Comptes Rendus Mathematique ( IF 0.8 ) Pub Date : 2019-06-01 , DOI: 10.1016/j.crma.2019.04.009
Bernd Ammann , Nadine Große , Victor Nistor

Abstract We prove well-posedness and regularity results for elliptic boundary value problems on certain singular domains that are conformally equivalent to manifolds with boundary and bounded geometry. Our assumptions are satisfied by the domains with a smooth set of singular cuspidal points, and hence our results apply to the class of domains with isolated oscillating conical singularities. In particular, our results generalize the classical L 2 -well-posedness result of Kondratiev for the Laplacian on domains with conical points. However, our domains and coefficients are too general to allow for singular function expansions of the solutions similar to the ones in Kondratiev's theory. The proofs are based on conformal changes of metric, on the differential geometry of manifolds with boundary and bounded geometry, and on our earlier geometric and analytic results on such manifolds.

中文翻译:

奇异域上的分析和边值问题:一种基于有界几何的方法

摘要 我们证明了特定奇异域上椭圆边值问题的适定性和正则性结果,这些奇异域与具有边界和有界几何的流形共形等价。我们的假设被具有一组平滑奇异尖点的域满足,因此我们的结果适用于具有孤立振荡圆锥奇点的域类。特别是,我们的结果概括了 Kondratiev 的经典 L 2 -适定性结果,用于具有圆锥点的域上的拉普拉斯算子。然而,我们的定义域和系数过于笼统,无法对类似于 Kondratiev 理论中的解的奇异函数展开。证明基于度量的共形变化,基于具有边界和有界几何的流形的微分几何,
更新日期:2019-06-01
down
wechat
bug