The thermistor obstacle problem with periodic data (Q2389059)

Summary: The object of this paper is the study of an obstacle thermistor problem with a nonlocal term. Using the classical Lax-Milgram theorem, a result of \textit{J. L. Lions} [Quelques méthodes de résolution des problemes aux limites non linéaires. (Paris) (1969; Zbl 0189.40603)] and a fixed point argument we prove existence of weak periodic solutions. Finally, by means of some a-priori estimates in Campanato's spaces, we obtain the regularity of these solutions.