Report
Higher-order chain rules for tensor fields, generalized Bell polynomials, and estimates in Orlicz-Sobolev-Slobodeckij and bounded variation spaces
| العنوان: | Higher-order chain rules for tensor fields, generalized Bell polynomials, and estimates in Orlicz-Sobolev-Slobodeckij and bounded variation spaces |
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| المؤلفون: | Licht, Martin W. |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Functional Analysis, 26B12 (Primary), 05A17, 26B30, 46E35, 49Q15 (Secondary) |
| الوصف: | We describe higher-order chain rules for multivariate functions and tensor fields. We estimate Sobolev-Slobodeckij norms, Musielak-Orlicz norms, and the total variation seminorms of the higher derivatives of tensor fields after a change of variables and determine sufficient regularity conditions for the coordinate change. We also introduce a novel higher-order chain rule for composition chains of multivariate functions that is described via nested set partitions and generalized Bell polynomials; it is a natural extension of the Fa\`a di Bruno formula. Our discussion uses the coordinate-free language of tensor calculus and includes Fr\'echet-differentiable mappings between Banach spaces. Comment: Submitted |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2212.11893 |
| رقم الانضمام: | edsarx.2212.11893 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |