Smooth Solutions of systems of quasilinear parabolic equations
Smooth Solutions of systems of quasilinear parabolic equations
复制标题
拟线性抛物型方程组的光滑解
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
J. Frehse
中科院分区：
文献类型：
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作者：
A. Bensoussan;J. Frehse
在这篇文章中，我们认为对角抛物系统的背景下产生的随机博弈。我们解决的问题，nding光滑的解决方案的系统。这样一个正则性结果对于证明一类随机对策的纳什点存在性的最优反馈是非常重要的。与标量方程的情况不同，一般情况下解的光滑性是达不到的。非线性哈密顿量的一种特殊结构似乎是实现正则性的适当结构。证明保持器解的存在性是该理论的关键步骤。数学学科分类。35XX，49XX。
We consider in this article diagonal parabolic systems arising in the context of stochastic dierential games. We address the issue of nding smooth solutions of the system. Such a regularity result is extremely important to derive an optimal feedback proving the existence of a Nash point of a certain class of stochastic dierential games. Unlike in the case of scalar equation, smoothness of solutions is not achieved in general. A special structure of the nonlinear Hamiltonian seems to be the adequate one to achieve the regularity property. A key step in the theory is to prove the existence of Holder solution. Mathematics Subject Classication. 35XX, 49XX.