Well-posedness of a nonlinear integro-differential problem and its rearranged formulation. (December 2016)

• Record Type: Journal Article
• Authors: Galiano, Gonzalo; Schiavi, Emanuele; Velasco, Julián
• Is Part Of: Nonlinear analysis. Volume 32(2016)
• Page Start: 74
• Page End: 90
• Publication Date: 2016-12
• Subjects: Integro-differential equation -- Existence and uniqueness -- Neighborhood filters -- Decreasing rearrangement -- Denoising -- Segmentation; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.03.013
• Languages: English
• ISSNs: 1468-1218

Abstract

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.