On the Robin problem in fractal domains

Local Fractal Interpolation On Unbounded Domains

We define fractal interpolation on unbounded domains for a certain class of topological spaces and construct local fractal functions. In addition, we derive some properties of these local fractal functions, consider their tensor products, and give conditions for local fractal functions on unbounded domains to be elements of Bochner-Lebesgue spaces.

Oscillatory integrals and periodic homogenization of Robin boundary value problems

In this paper, we consider a family of second-order elliptic systems subject to a periodically oscillating Robin boundary condition. We establish the qualitative homogenization theorem on any Lipschitz domains satisfying a non-resonance condition. We also use the quantitative estimates of oscillatory integrals to obtain the dimension-dependent convergence rates in $L^2$, assuming that the domain is smooth and strictly convex.

粗糙区域上Robin调和测度的维数与结构

Dimension and structure of the Robin Harmonic Measure on Rough Domains

研究粗糙区域Robin调和测度的维数与结构，证明其对Ahlfors正则集曲面测度具定量相互绝对连续性，无维数下降，预期相变通过非尺度不变权重估计体现，颠覆相关物理模拟预期。