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Seminar on Analysis, Differential Equations and Mathematical Physics
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Weakly Lipschitz mappings in higher dimensions A. Golberg Holon Academic Institute of Technology |
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Abstract: In one dimension, Lipschitz continuity serves as a natural bridge between continuous differentiability and absolute continuity. However, this relatively simple picture becomes significantly more intricate in higher dimensions. Despite this added complexity, Lipschitz mappings retain a wealth of important properties and find numerous applications. Classical results, such as the McShane and Kirszbraun extension theorems, alongside the preservation of Hausdorff dimension, underscore the significance of these mappings. This talk delves into the fascinating and multifaceted theory of Lipschitz functions in the higher-dimensional setting. We will introduce a weakly Lipschitz condition and establish that such a mapping is absolutely continuous on almost all lines parallel to the coordinate axes (an ACL-mapping) and belongs to the Sobolev class Language: English Website: https://msrn.tilda.ws/sl |
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