Publications [#385681] of Hanye Zhu

Papers Published

1. Dong, H; Yang, Z; Zhu, H, Gradient estimates for the conductivity problem with imperfect bonding interfaces, Journal Fur Die Reine Und Angewandte Mathematik, vol. 2026 no. 830 (January, 2026), pp. 101-139 [doi]
   (last updated on 2026/01/17)

   Abstract:
   We study the field concentration phenomenon between two closely spaced perfect conductors with imperfect bonding interfaces of low conductivity type. The boundary condition on these interfaces is given by a Robin-type boundary condition. We discover a new dichotomy for the field concentration depending on the bonding parameter y. Specifically, we show that the gradient of solution is uniformly bounded independent of E (the distance between two inclusions) when y is sufficiently small. However, the gradient may blow up when y is large. Moreover, we identify the threshold of y and the optimal blow-up rates under certain symmetry assumptions. The proof relies on a crucial anisotropic gradient estimate in the thin neck between two inclusions. We develop a general framework for establishing such estimate, which is applicable to a wide range of elliptic equations and boundary conditions.