YONSEI Math-CSE Colloquium
2021. 10. 21. (목) 17 : 00
Geometric Series Expansions of Layer Potential Operators and Their Applications to Composite Materials
For a simply connected planar domain, there exists a function that conformally maps a region outside a circular disk to the region outside the domain. This conformal mapping then defines the so-called Faber polynomials, which form a basis for analytic functions. The Neumann–Poincaré (NP) operator, a singular integral operator on the boundary of a domain, naturally appears when one solves a conductivity transmission problem via the boundary integral formulation. In this talk, I present the geometric series expressions for the NP operator and the single-layer potential in two dimensions using the Faber polynomials. I will then provide some geometric properties of composite materials obtained with the series expansions, including the effective conductivity of a periodic array of inclusions with extremal conductivity and extension of theEshelby conjecture to domains of general shape for anti-plane elasticity.
Zoom link
https://yonsei.zoom.us/j/89486652536?pwd=VFhRcjd0dWJWZlozY1RZa0xPUGIrZz09
Meeting ID: 894 8665 2536
Passcode: 224718