On the Cahn-Hilliard equation with dynamic boundary conditions and a dominating boundary potential

The Cahn-Hilliard and viscous Cahn-Hilliard equations with singular and possibly nonsmooth potentials and dynamic boundary condition are considered and some well-posedness and regularity results are proved. Key words: Cahn-Hilliard equation, dynamic boundary conditions, phase separation, irregular potentials, well-posedness.Comment: A revised version of this paper has been published on J. Math. Anal. Appl. 419 (2014), 972-994: the authors would like to point out that both the published version and the arXiv preprint contain a useless assumption in formula (2.37), concerning the zero normal derivative of the initial value on the boundary; indeed this condition is never employed in the proof

Representation of maxitive measures: an overview

Idempotent integration is an analogue of Lebesgue integration where $\sigma$-maxitive measures replace $\sigma$-additive measures. In addition to reviewing and unifying several Radon--Nikodym like theorems proven in the literature for the idempotent integral, we also prove new results of the same kind.Comment: 40 page