论文标题
通过轴对称域中的傅立叶系数来表征Sobolev空间
Characterization of Sobolev spaces by their Fourier coefficients in axisymmetric domains
论文作者
论文摘要
使用轴对称域上函数的傅立叶级数表示，我们发现函数的傅立叶系数的加权SOBOLEV规范产生的范围等于该函数的标准Sobolev规范。从等效常数独立于域，这种特征是普遍的。特别是统一是域是否包含其旋转轴的一部分，还是与轴的一部分是不相交的，但可能是任意接近轴的。我们使用涉及到轴距离的加权规范的表征与书中先前获得的距离[Bernardi，Dauge，Maday“轴对称结构域的光谱方法”，Gauthier-Villars，1999]，涉及痕量条件，是范围依赖的。我们还为LOC中给出的证据的非圆柱域提供了补充。引用。
Using Fourier series representations of functions on axisymmetric domains, we find weighted Sobolev norms of the Fourier coefficients of a function that yield norms equivalent to the standard Sobolev norms of the function. This characterization is universal in the sense that the equivalence constants are independent of the domain. In particular it is uniform whether the domain contains a part of its axis of rotation or is disjoint from, but maybe arbitrarily close to, the axis. Our characterization using step-weighted norms involving the distance to the axis is different from the one obtained earlier in the book [Bernardi, Dauge, Maday "Spectral methods for axisymmetric domains", Gauthier-Villars, 1999], which involves trace conditions and is domain dependent. We also provide a complement for non cylindrical domains of the proof given in loc. cit. .
