Generalized Reduced Modulus in Euclidean Space
A. S. Afanaseva-Grigoreva, K. A. Gulyaeva, E. G. Prilepkina · Lobachevskii Journal of Mathematics · 2024
Abstract In an Euclidean space, we study condensers with variable potential levels and the presence of a free part at the boundary. The asymptotic formula for the modulus of such condenser is obtained when the plates shrink to points. The generalized reduced modulus is defined as the second term of this asymptotics. We establish a relation between the reduced modulus and the discrete energy of the Robin function, and investigate its monotonicity and behavior under polarization.