Classical global solutions for a class of Hamilton-Jacobi equations

被引：0

作者：

Cruz-Sampedro J. ^{[1
]}

机构：

[1] Departamento de Ciencias Básicas, UAM-A, Col Reynosa Tamaulipas, Mexico, D.F. 02200

来源：

Qualitative Theory of Dynamical Systems | 2009年 / 8卷 / 2期

关键词：

Eikonal equation; Global solution; Hamilton-Jacobi equation;

D O I：

10.1007/s12346-010-0017-6

中图分类号：

学科分类号：

摘要：

Let V be a real-valued function of class C2 on ℝn, n ≥ 2, which vanishes if {pipe}x{pipe} ≤ R and, for some ∈ > 0, satisfies ∂αx V(x) = O({pipe}x{pipe}-∈-{pipe}α{pipe}), as {pipe}x{pipe} → ∞, for {pipe}α{pipe} ≤ 2. Using a global inverse function theorem of Hadamard, we showthat if R is sufficiently large, then the Hamilton-Jacobi equation of eikonal type {pipe}∇u{pipe}2+V(x) = k2, with k > 0, has a C1 solution on ℝn {0}. © Birkhäuser/Springer Basel AG 2010.

引用

页码：267 / 277

页数：10

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