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In a series of papers on optimal control problems for the monodomain as wellas for the bidomain equations of cardiac electrophysiology, the authors studiedexistence of minimizers and derived first-order necessary optimalityconditions. The analysis of these control problems is based on a regularitydiscussion for weak solutions, resulting in a stability estimate and auniqueness theorem for the monodomain and bidomain system, respectively.Unfortunately, the authors recognized a serious error within the proof of thesetheorems. However, the present investigation shows that the assertions from[Kunisch/Wagner 12] and [Kunisch/Wagner 13a] can be maintained (with minorchanges only) while the proofs must be subjected to considerable alterations.As a consequence, the optimization theorems from [Kunisch/Wagner 13b] allow forsubstantial improvements. Therefore, in the present paper we provide a refinedregularity discussion of the bidomain system together with corrected proofs.

Optimal control of the bidomain system (IV): Corrected proofs of the stability and regularity theorems