Gradient and Hessian regularity in elliptic transmission problems near a point cusp
arxiv(2024)
摘要
We consider elliptic transmission problems in several space dimensions near
an interface which is C^1,1 diffeomorphic to an axisymmetric
reference-interface with a singular point of cusp type. We establish the
regularity of the gradient and of the Hessian in L^p spaces up to the cusp
point for local weak solutions. We obtain regularity thresholds which are
different according to whether the cusp is inward or outward to the subdomain,
and which depend explicitly on the opening of the interface at the cusp. Our
results allow for source terms in the bulk and on the interface.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要