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| Name | Euclidean Sobolev Functions—Key Properties |
| Video Uploader | Video From Young Measures |
| Upload Date | This Video Uploaded At 27-06-2023 10:20:34 |
| Video Discription | What does it take for function to be in the Sobolev space? What more is true about a Sobolev function than a merely measurable (integrable) function? In the Euclidean setting answering this question fill up a volume or two of a book! In this video I attempt to squeeze it down into 5 main properties: a) Sobolev spaces are Banach spaces and bounded sequences have (weakly) convergent subsequences. b) Sobolev embeddings (aka inequalities) give higher integrability of functions than their definition gives, c) They are absolutely continuous on almost all rectifiable curves, (the stronger form of the more famous ACL characterization of Sobolev functions), d) Their fine properties in terms of capacities, their quasicontinuity, e) Density of Lipschitz functions in them. Many of these properties are meaningful and well-defined questions can be formulated about them in the general metric measure space setting. So, in developing theories of Sobolev spaces on mms we should keep such questions in mind. The choices we make are guided by what properties we wish to retain in such generalizations. Thanks for watching and please subscribe. #geometricconstruction #metricspace #mathematicalanalysis #fractals #measure #sobolev #borel #dirichlet #PDE |
| Category | Education |
| Tags | Education Download MP4 | Education Download MP3 | Education Download MP4 360p | Education Download MP4 480p | Education Download MP4 720p | Education Download MP4 1080p |
