Equivalence of viscosity and weak solutions for a p-parabolic equation

被引：7
|
作者：
Siltakoski, Jarkko [1 ]
机构：
[1] Univ Jyvaskyla, Dept Math & Stat, POB 35, Jyvaskyla 40014, Finland
来源：
JOURNAL OF EVOLUTION EQUATIONS | 2021年 / 21卷 / 02期
关键词：
Comparison principle; Gradient term; Parabolic p-Laplacian; Viscosity solution; Weak solution; SUPERSOLUTIONS; REGULARITY; BOUNDARY; MAXIMUM;
D O I：
10.1007/s00028-020-00666-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the relationship of viscosity and weak solutions to the equation partial derivative(t)u - Delta(p)u = f (Du), where p > 1 and f is an element of C(R-N) satisfies suitable assumptions. Our main result is that bounded viscosity supersolutions coincide with bounded lower semicontinuous weak supersolutions. Moreover, we prove the lower semicontinuity of weak supersolutions when p >= 2.
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页码：2047 / 2080
页数：34
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