A fractional Korn-type inequality
A fractional Korn-type inequality
复制标题
分数科恩型不等式
DOI：
--
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
T. Mengesha
中科院分区：
文献类型：
--
作者：
J. Scott;T. Mengesha
我们证明，其半范数涉及“方向”差商的大小的一类向量场空间实际上等价于分数索博列夫空间类。该等价可以被认为是分数 Sobolev 空间的 Korn 型表征。我们利用该结果更好地理解与通过近场动力学与非局部连续介质模型相关的强耦合非局部方程组相关的能量空间。此外，等价性允许我们应用经典空间嵌入来证明非局部系统的弱解具有改进的可微性和改进的可积性。
We show that a class of spaces of vector fields whose semi-norms involve the magnitude of "directional" difference quotients is in fact equivalent to the class of fractional Sobolev spaces. The equivalence can be considered a Korn-type characterization of fractional Sobolev spaces. We use the result to understand better the energy space associated to a strongly coupled system of nonlocal equations related to a nonlocal continuum model via peridynamics. Moreover, the equivalence permits us to apply classical space embeddings in proving that weak solutions to the nonlocal system enjoy both improved differentiability and improved integrability.