Existence and regularity of capacity solutions for a strongly coupled system derived from a thermistor problem

Abstract

This paper explores strongly parabolic-elliptic systems within Orlicz–Sobolev spaces. It introduces the concept of capacity solutions and emphasizes the establishment of existence and regularity of solutions through rigorous proofs. Specifically, it addresses the existence of capacity solutions for a strongly nonlinear coupled system without reliance on the \(\Delta _2\)-condition for the N-function. This system, akin to a modified thermistor problem, concerns the determination of variables representing the temperature within a conductor and the associated electrical potential.