Some integral inequalities with applications to the imbedding of Sobolev spaces defined over irregular domains
Some integral inequalities with applications to the imbedding of Sobolev spaces defined over irregular domains
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一些积分不等式及其在不规则域上定义的 Sobolev 空间嵌入的应用
DOI：
10.1090/s0002-9947-1973-0322494-0
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发表时间：
1973
影响因子：
1.3
通讯作者：
R. Adams
中科院分区：
文献类型：
--
作者：
R. Adams
本文探讨了将Sobolev嵌入定理推广到某些不具有该定理所要求的“锥性质”的域的可能性。它表明，没有扩展是可能的某些类型的域（例如，指数尖锐的尖点或无界的，有有限的体积），而其他类型（域尖锐尖点少）的扩展。这些结果是通过某些积分不等式，推广不平等由于哈代和索博列夫，并在自己的权利有一定的兴趣。本文分为两个部分。第一部分建立积分不等式;第二部分处理嵌入定理的扩展。进一步的介绍性信息可在每一部分的第一节中找到。第一部分.积分不等式1.
This paper examines the possibility of extending the Sobolev Imbedding Theorem to certain classes of domains which fail to have the "cone property" normally required for that theorem. It is shown that no extension is possible for certain types of domains (e.g. those with exponentially sharp cusps or which are unbounded and have finite volume), while extensions are obtained for other types (domains with less sharp cusps). These results are developed via certain integral inequalities which generalize inequalities due to Hardy and to Sobolev, and are of some interest in their own right. The paper is divided into two parts. Part I establishes the integral inequalities; Part II deals with extensions of the imbedding theorem. Further introductory information may be found in the first section of each part. PART I. INTEGRAL INEQUALITIES 1.