Higher differentiability in the context of Besov spaces for a class of nonlocal functionals
Higher differentiability in the context of Besov spaces for a class of nonlocal functionals
复制标题
一类非局部泛函在 Besov 空间背景下具有更高的可微性
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Joe Geisbauer
中科院分区：
文献类型：
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作者：
M. Foss;Joe Geisbauer
本文的目的是通过研究两类非局部泛函，为变分法中的非局部理论做出贡献。由于非局部理论不像局部理论那样发展，因此给出了极小元存在唯一性的证明。然而，本文的主要结果建立了更高的可微性，在Besov空间的背景下，为非局部泛函的极小。这个结果是在二次增长假设下通过差商方法得到的。
The aim of this paper is to contribute to the nonlocal theory within the calculus of variations by studying two classes of nonlocal functionals. Since the nonlocal theory is not quite as developed as the local theory, a proof for the existence and uniqueness of minimizers is provided. However, the main result within the paper establishes the higher differentiability, in the context of Besov spaces, for minimizers of nonlocal functionals. This result is obtained under quadratic growth assumptions via the difference quotient method.