Differentiable Functions on Bad Domains
Differentiable Functions on Bad Domains
复制标题
坏域上的可微分函数
DOI：
10.1142/3197
复制
发表时间：
1998
期刊：
影响因子：
--
通讯作者：
S. Poborchi
中科院分区：
文献类型：
--
作者：
V. Maz'ya;S. Poborchi
第一部分：良好域或一般域上的Sobolev空间：Sobolev函数的密度定理、扩张定理和Poincare不等式，Sobolev型嵌入定理及其应用，嵌入定理和等周不等式。第二部分奇依赖于参数的域的Sobolev空间：定义在参数依赖域上的函数的延拓，边界的参数依赖分量上具有一阶导数的函数的迹。第三部分尖点域上的Sobolev空间：函数到顶点在边界上的区域外的扩张尖点域上的Sobolev空间的嵌入定理尖点域边界上的Sobolev空间中函数的迹。
Part 1 Sobolev spaces for good or general domains: density theorems, extension theorems and Poincare's inequality for Sobolev functions imbedding theorems of Sobolev type and their applications imbedding theorems and isoperimetric inequalities. Part 2 Sobolev spaces for domains singularly depending on parameters: extension of functions defined on parameter dependent domains traces of functions with first derivatives on parameter dependent components of a boundary. Part 3 Sobolev spaces for domains with cusps: extension of functions to the exterior of a domain with the vertex of a peak on the boundary imbedding theorems for Sobolev spaces in domains with cusps traces of functions in Sobolev spaces on the boundary of a domain with a cusp.