On the Dirichlet Problem for the One-Dimensional Rudin–Osher–Fatemi Functional

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-07-31 DOI:10.1002/mma.70014

Piotr Rybka

引用次数: 0

Abstract

We provide a number of sufficient conditions for those minimizers of the one-dimensional Rudin–Osher–Fatemi functional that satisfy the Dirichlet data in the trace sense. For this purpose, we use results specific for the total variation flow. We also show a number of counterexamples.

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一维Rudin-Osher-Fatemi泛函的Dirichlet问题

给出了一维Rudin-Osher-Fatemi泛函在迹意义上满足Dirichlet数据的极小值的若干充分条件。为此，我们使用特定于总变化流的结果。我们还展示了一些反例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.