GENERALIZATIONS OF LOGARITHMIC SOBOLEV INEQUALITIES

被引：15
|
作者：
Merker, Jochen [1 ]
机构：
[1] Univ Rostock, Inst Math, Univ Pl 1, D-18051 Rostock, Germany
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2008年 / 1卷 / 02期
关键词：
p-Laplacian; doubly nonlinear evolution equations; ultracontractive semigroups; logarithmic Gagliardo-Nirenberg inequalities;
D O I：
10.3934/dcdss.2008.1.329
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We generalize logarithmic Sobolev inequalities to logarithmic Gagliardo-Nirenberg inequalities, and apply these inequalities to prove ultracontractivity of the semigroup generated by the doubly nonlinear p-Laplacian (u)over dot = Delta(p)u(m). Our proof does not use Moser iteration, but shows that the time-dependent Lebesgue norm parallel to u(t)parallel to(r(t)) stays bounded for a variable exponent r(t) blowing up in arbitrary short time.
引用
收藏
页码：329 / 338
页数：10
相关论文
共 50 条
12345