Wellposedness of a nonlocal nonlinear diffusion equation of image processing

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• 作者：Patrick Guidotti^a ; ^{gpatrick@math.uci.edu} ; Yuanzhen Shao^b ; ^{shao92@purdue.edu}
• 关键词：35A01 ; 35A02 ; 35B40 ; 35K55 ; 35K65
• 刊名：Nonlinear Analysis: Theory, Methods & Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：150
• 期：Complete
• 页码：114-137
• 全文大小：781 K
• 卷排序：150

文摘

Existence and uniqueness of solutions to non-smooth initial data are established for a slight modification of the degenerate regularization of the well-known Perona–Malik equation first proposed in Guidotti and Lambers (2009). The results heavily rely on the choice of an appropriate functional setting inspired by a recent approach to degenerate parabolic equations via so-called singular Riemannian manifolds (Amann, 2013, 2016).