Gradient estimates for the insulated conductivity problem

Abstract: In this talk, we discuss the insulated conductivity problem with multiple inclusions embedded in a bounded domain in $n$-dimensional Euclidean space. The gradient of a solution may blow up as two inclusions approach each other. The optimal blow up rate was known in dimension $n=2$. It was not known whether the established upper bound of the blow up rates in higher dimensions were optimal. We answer this question by improving the previously known upper bound of the blow up rates in dimension $n>2$. This is a joint work with Zhuolun Yang.

analysis of PDEs

Audience: researchers in the topic

Rio de Janeiro webinar on analysis and partial differential equations

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