On the second-order regularity of solutions to the parabolic p-Laplace equation

被引：2
|
作者：
Feng, Yawen [1 ,2 ]
Parviainen, Mikko [1 ]
Sarsa, Saara [3 ]
机构：
[1] Univ Jyvaskyla, Dept Math & Stat, POB 35, Jyvaskyla 40014, Finland
[2] Beihang Univ, Sch Math Sci, Shahe Higher Educ Pk South Third St 9, Beijing 102206, Peoples R China
[3] Univ Helsinki, Dept Math & Stat, POB 68,Pietati Kalmin Katu 5, Helsinki 00014, Finland
来源：
JOURNAL OF EVOLUTION EQUATIONS | 2022年 / 22卷 / 01期
关键词：
p-parabolic functions; Weak solutions; Fundamental inequality; Sobolev regularity; Time derivative; EQUIVALENCE; GRADIENT;
D O I：
10.1007/s00028-022-00760-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the second-order Sobolev regularity of solutions to the parabolic p-Laplace equation. For any p-parabolic function u, we show that D(vertical bar Du vertical bar(p-2+s/2) Du) exists as a function and belongs to L-loc(2) with s > -1 and 1 < p < infinity. The range of s is sharp.
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页数：17
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