The Space Hp of Solutions of Degenerate Parabolic Equations

被引：0
|
作者：
Kapitsyna, T. V. [1 ]
机构：
[1] Natl Res Univ, Moscow Power Engn Inst, Moscow 111250, Russia
来源：
MATHEMATICAL NOTES | 2023年 / 114卷 / 5-6期
关键词：
degenerate parabolic equation; Second-order equation; boundary values in the sense of L-2; Lyapunov boundary; initial and boundary conditions;
D O I：
10.1134/S0001434623110159
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In a cylinder Q whose base is bounded by a Lyapunov surface, a second-order parabolic equation degenerate in the tangent directions to the boundary of the base is considered. For solutions of this equation, a class H-p is introduced by analogy with the elliptic case. A criterion for a function to belong to this class is found. Conditions for the unique solvability of the problem with boundary and initial conditions understood in the sense of L(p )are given.
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收藏
页码：797 / 803
页数：7
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