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arXiv · 2111.13942

Leibniz rules and Gauss-Green formulas in distributional fractional spaces

Giovanni E. Comi·Giorgio Stefani
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Abstract

We apply the results established in arXiv:2109.15263 to prove some new fractional Leibniz rules involving $BV^{\alpha,p}$ and $S^{\alpha,p}$ functions, following the distributional approach adopted in the previous works arXiv:1809.08575, arXiv:1910.13419, arXiv:2011.03928. In order to achieve our main results, we revise the elementary properties of the fractional operators involved in the framework of Besov spaces and we rephraze the Kenig-Ponce-Vega Leibniz-type rule in our fractional context. We apply our results to prove the well-posedness of the boundary-value problem for a general $2\alpha$-order fractional elliptic operator in divergence form.

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BibTeXRIS

Giovanni E. Comi, Giorgio Stefani. 2021-11-27. Leibniz rules and Gauss-Green formulas in distributional fractional spaces. https://doi.org/10.1016/j.jmaa.2022.126312

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