Hölder estimates in space‐time for viscosity solutions of hamilton‐jacobi equations
Hölder estimates in space‐time for viscosity solutions of hamilton‐jacobi equations
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Hölder 对 Hamilton-Jacobi 方程粘度解的时空估计
DOI：
10.1002/cpa.20315
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发表时间：
2009
影响因子：
3
通讯作者：
P. Cardaliaguet
中科院分区：
文献类型：
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作者：
P. Cannarsa;P. Cardaliaguet
众所周知，当拉格朗日依赖于t时，变分中基本问题的解可能不是Lipschitz连续的。同样，对于含时的Hamilton-Jacobi方程的粘性解，人们不能期望Lipschitz界关于系数的正则性一致地保持。这一现象引发了这样一个问题：这种解是否满足某种较弱范数下的一致估计。我们将证明这是适当的Hölder范数的情况，得到关于一阶和二阶Hamilton-Jacobi方程的解在(x，t)中的一致估计。我们的结果适用于退化的抛物型方程，并且要求哈密顿量在无穷远的梯度变量中超线性增长。证明基于粘性解的比较变元和表示式，以及弱逆Hölder不等式。©2010 Wiley期刊，Inc.
It is well‐known that solutions to the basic problem in the calculus of variations may fail to be Lipschitz‐continuous when the Lagrangian depends on t. Similarly, for viscosity solutions to time‐dependent Hamilton‐Jacobi equations one cannot expect Lipschitz bounds to hold uniformly with respect to the regularity of coefficients. This phenomenon raises the question whether such solutions satisfy uniform estimates in some weaker norm. We will show that this is the case for a suitable Hölder norm, obtaining uniform estimates in (x,t) for solutions to first‐ and second‐order Hamilton‐Jacobi equations. Our results apply to degenerate parabolic equations and require superlinear growth at infinity, in the gradient variables, of the Hamiltonian. Proofs are based on comparison arguments and representation formulas for viscosity solutions, as well as weak reverse Hölder inequalities. © 2010 Wiley Periodicals, Inc.
粘性 Hamilton-Jacobi 方程和相关扩散过程
DOI：
--
发表时间：
2010
期刊：
影响因子：
--
作者：
Mukaihira;Y. Mori;K. Kondo;近藤弘一;Naoyuki Ichihara;近藤弘一;Naoyki Ichihara
通讯作者：
Naoyki Ichihara