AI 中文总结
研究高电导率类型不完全粘结的中性夹杂，证明若此类夹杂对所有均匀场呈中性则其为椭圆或椭球，通过边界面上微分方程解的存在性给出中性条件，转化为代数边界恒等式来证明主要结果。
AI 中文摘要
本文关注高电导率类型不完全粘结的中性夹杂。一个作为有界区域的夹杂，若通量沿其边界不连续而电势连续，则称其为高电导率类型不完全粘结。若夹杂的存在不干扰其外部场，则该夹杂对均匀场是中性的。已知通过在边界引入适当的不完全粘结系数，椭圆和椭球可对所有均匀场呈中性。本文目的是证明其逆命题。我们证明若高电导率类型不完全粘结的夹杂对所有均匀场呈中性，则它是椭圆或椭球。中性条件由边界面上某微分方程解的存在性给出，主要结果通过将中性条件转化为表征椭圆和椭球的代数边界恒等式来证明。
英文摘要
This paper concerns neutral inclusions for imperfect bonding of high-conductivity type. An inclusion, which is a bounded domain, is said to be of imperfect bonding of high-conductivity type if the flux is discontinuous along its boundary while the potential is continuous. The inclusion is neutral to a uniform field if the presence of the inclusion does not perturb the field outside the inclusion. It is known that ellipses and ellipsoids can be neutral to all uniform fields by introducing a proper imperfect bonding coefficient on boundaries. The purpose of this paper is to prove the converse. We prove that if an inclusion of imperfect bonding of high-conductivity type is neutral to all uniform fields, then it is an ellipse or an ellipsoid. The neutrality condition is given by existence of the solution to a certain differential equation on the boundary surface and the main result is proved by converting the neutrality condition into an algebraic boundary identity characterizing ellipses and ellipsoids.
Comments13 pages
