Well-posedness of a nonlinear integro-differential problem and its rearranged formulation
arXiv:1506.02247 · doi:10.1016/j.nonrwa.2016.03.013
Abstract
We study the existence and uniqueness of solutions of a nonlinear integro-differential problem which we reformulate introducing the notion of the decreasing rearrangement of the solution. A dimensional reduction of the problem is obtained and a detailed analysis of the properties of the solutions of the model is provided. Finally, a fast numerical method is devised and implemented to show the performance of the model when typical image processing tasks such as filtering and segmentation are performed.
Final version. To appear in Nolinear Analysis Real World Applications (2016)