论文标题
基本上完全各向异性的Orlicz功能和唯一性来测量数据问题
Essentially fully anisotropic Orlicz functions and uniqueness to measure data problem
论文作者
论文摘要
通过强烈的非线性操作员研究椭圆度量的数据问题，其增长是通过完全各向异性$ n $功能的方式来描述的，我们证明了广泛措施的独特性。为了提供它，开发了完全各向异性Orlicz-Sobolev空间中能力的框架，并给出了〜有界度量的〜2。 此外，我们举例说明了各向异性的年轻函数$φ$，使得$ |ξ| eD |^p \lysSimφ（ξ）\ sillsim | sim | eC^p \ log^log^α（1+|ξ|）$，任意$ p \ geq 1 $，$α> 0 $，但不符合规定，我们称呼为“ $ a”，但要完全不符合我们的and。实际上，由$φ$生成的Orlicz--sobolev-型空间不可或缺需要完全各向异性工具才能处理。
Studying elliptic measure data problem with strongly nonlinear operator whose growth is described by the means of fully anisotropic $N$-function, we prove the uniqueness for a broad class of measures. In order to provide it, the framework of capacities in fully anisotropic Orlicz-Sobolev spaces is developed and the~capacitary characterization of a~bounded measure is given. Moreover, we give an example of an anisotropic Young function $Φ$, such that $|ξ|^p \lesssimΦ(ξ)\lesssim |ξ|^p\log^α(1+|ξ|)$, with arbitrary $p\geq 1$, $α>0$, but so irregularly growing that % we call it essentially fully anisotropic. In fact, the Orlicz--Sobolev--type space generated by $Φ$ indispensably requires fully anisotropic tools to be handled.
