An extension of the Eshelby conjecture to domains of general shape in anti-plane elasticity

According to the Eshelby conjecture, an ellipse or ellipsoid is only shape that induces interior uniform strain under a far-field loading. We extend conjecture domains of general for anti-plane elasticity. Specifically, we show each positive integer N , inclusion polynomial loading degree if and exterior conformal map Laurent series . Furthermore, isotropic case, characterize by using first-degree explicitly solve potential in terms Grunsky coefficients.