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.

引用

页数：17

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