Stochastic Homogenization for Functionals with Anisotropic Rescaling and Noncoercive Hamilton-Jacobi Equations
Stochastic Homogenization for Functionals with Anisotropic Rescaling and Noncoercive Hamilton-Jacobi Equations
复制标题
具有各向异性缩放和非强制哈密顿-雅可比方程的泛函随机齐次化
DOI：
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发表时间：
2017
影响因子：
2
通讯作者：
Claudio Marchi
中科院分区：
文献类型：
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作者：
N. Dirr;F. Dragoni;Paola Mannucci;Claudio Marchi
本文研究了一类一阶Hamilton-Jacobi方程Cauchy问题的随机均匀化，其算子不是强制性的。梯度变量。我们看看像$H（x，sigma（x）p，omega）$这样的哈密顿量，其中$sigma（x）$是与卡诺群相关联的矩阵。考虑的重标度是一致的基本卡诺群结构，因此各向异性。我们将证明，在适当的假设下的哈密顿量，解决方案的$varepados $-问题收敛到一个确定性的功能，可以描述为一个合适的确定性的哈密顿-雅可比问题的唯一（粘性）解决方案。
We study the stochastic homogenization for a Cauchy problem for a first-order Hamilton-Jacobi equation whose operator is not coercive w.r.t. the gradient variable. We look at Hamiltonians like $H(x,sigma(x)p,omega)$ where $sigma(x)$ is a matrix associated to a Carnot group. The rescaling considered is consistent with the underlying Carnot group structure, thus anisotropic. We will prove that under suitable assumptions for the Hamiltonian, the solutions of the $varepsilon$-problem converge to a deterministic function which can be characterized as the unique (viscosity) solution of a suitable deterministic Hamilton-Jacobi problem.