Inpainting is the action of restoring missing or damaged details in images, and it is desirable to produce a result, which to the naked eye, does not distinguish where the inpainting has been performed. Out of the many existing approaches and algorithms proposed in the literature, we focus on the approach of Bertozzi, Esedoglu and Gillette that modifies the Cahn-Hilliard equation with a data fidelity term. This method seems to be simpler to implement and obtain good reconstruction much faster. We alter the potential term from a smooth quartic one to a non-smooth one and discuss the existence of solutions to both the time-dependent and stationary problems.  This is a joint work with Harald Garcke (Regensburg) and Vanessa Styles (Sussex).

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