Regularity in Sobolev spaces for doubly nonlinear parabolic equations

被引：6
作者：
Ebmeyer, C
Urbano, JM
机构：
[1] Univ Bonn, Math Seminar, D-53115 Bonn, Germany
[2] Univ Coimbra, Dept Matemat, P-3001454 Coimbra, Portugal
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2003年 / 187卷 / 02期
关键词：
degenerate parabolic equation; porous medium equation; p-Laplacian; finite speed of propagation; difference quotient;
D O I：
10.1016/S0022-0396(02)00093-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The doubly nonlinear parabolic equation u(t) = div[\del(\u\(m-1)u)\(p-2)del(\u\(m-1)u)] (m > 1, m(p - 1) > 1) is considered in several dimensions and regularity results in fractional order Sobolev spaces are obtained. The main tools in the proof are a difference quotient technique and the imbedding theorem of Nikolskii spaces into Sobolev spaces. (C) 2002 Elsevier Science (USA). All rights reserved.
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页码：375 / 390
页数：16
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