UNIFORM POINCARE INEQUALITY IN O-MINIMAL STRUCTURES

被引：2
|
作者：
Valette, Anna
Valette, Guillaume
机构：
[1] Uniwersytet Jagielloński Katedra Teorii Optymalizacji i Sterowania Wydział Matematyki i Informatyki, ul. S. Łojasiewicza 6, Kraków
[2] Uniwersytet Jagielloński Instytut, Matematyki ul. S. Łojasiewicza 6, Kraków
来源：
MATHEMATICAL INEQUALITIES & APPLICATIONS | 2023年 / 26卷 / 01期
关键词：
Poincare?inequality; Sobolev spaces; singular domains; subanalytic functions; o-minimal structures;
D O I：
10.7153/mia-2023-26-11
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We first define the trace on a domain omega which is definable in an o-minimal structure. We then show that every function u is an element of W1,p(omega) vanishing on the boundary in the trace sense satisfies Poincare ' inequality. We finally show, given a definable family of domains (omega t)t is an element of Rk , that the constant of this inequality remains bounded, if so does the volume of omega t .
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页码：141 / 142
页数：2
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