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arXiv · 1506.02247

Well-posedness of a nonlinear integro-differential problem and its rearranged formulation

Gonzalo Galiano·Emanuele Schiavi·Julián Velasco
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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.

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Gonzalo Galiano, Emanuele Schiavi, Julián Velasco. 2015-06-07. Well-posedness of a nonlinear integro-differential problem and its rearranged formulation. https://doi.org/10.1016/j.nonrwa.2016.03.013

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