Uniqueness and regularity of weak solutions of a drift-diffusion system for perovskite solar cells

TL;DR

This paper proves a new uniqueness result for a drift-diffusion model of perovskite solar cells, enhancing understanding of charge transport and ionic vacancy behavior using advanced regularity techniques.

Contribution

It introduces a novel uniqueness proof for the model, leveraging improved gradient integrability and regularity results for the associated equations.

Findings

Established uniqueness of weak solutions for the model

Demonstrated improved integrability of charge-carrier gradients

Applied advanced regularity results to the drift-diffusion system

Abstract

We establish a novel uniqueness result for an instationary drift-diffusion model for perovskite solar cells. This model for vacancy-assisted charge transport uses Fermi--Dirac statistics for electrons and holes and Blakemore statistics for the mobile ionic vacancies in the perovskite. Existence of weak solutions and their boundedness was proven in a previous work. For the uniqueness proof, we establish improved integrability of the gradients of the charge-carrier densities. Based on estimates obtained in the previous paper, we consider suitably regularized continuity equations with partly frozen arguments and apply the regularity results for scalar quasilinear elliptic equations by Meinlschmidt & Rehberg, Evolution Equations and Control Theory, 2016, 5(1):147-184.