A Mixed Formulation Approach to the p-Curl Problem: Well-Posedness Analysis

Abstract

This paper establishes the existence, uniqueness, and stability of solutions for a mixed variational formulation in three dimensions of the p-curl problem, a nonlinear model describing the behavior of magnetic fields in type II high-temperature superconductors (HTS). The problem exhibits strong mathematical parallels with the p-Laplacian. In our previous work, we constructed the Hellinger–Reissner functional for this problem and identified two distinct functional frameworks in which to seek solutions, successfully proving well-posedness for the first case. The present work completes this analysis by establishing well-posedness for the second, more mathematically challenging framework under homogeneous boundary conditions, thereby extending the theoretical foundation for numerical approximations of the solution.