Optimizing the fundamental Neumann eigenvalue for the Laplacian in a domain with small traps

Abstract

An optimization problem for the fundamental eigenvalue . This optimization problem is found to be directly related to an oxygen transport problem in skeletal muscle tissue, and to determining equilibrium locations of spikes to the Gierer–Meinhardt reaction-diffusion model. It is also closely related to the problem of determining equilibrium vortex configurations within the context of the Ginzburg–Landau theory of superconductivity.