Some remarks on quasi-variational inequalities and the associated impulsive control problem
Some remarks on quasi-variational inequalities and the associated impulsive control problem
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关于拟变分不等式及相关脉冲控制问题的一些评论
DOI：
10.1016/s0294-1449(16)30404-8
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发表时间：
1985
期刊：
影响因子：
--
通讯作者：
B. Perthame
中科院分区：
文献类型：
--
作者：
B. Perthame
本文研究拟变分不等式：（1）{Max（A u-f，u-M u）= 0，u|其中（2）Mu = k+ inf ∈ Ω <$<${c0（k）+ u（x+ k）}.在一般情况下，（1）没有解，我们在这里证明（1）有一个唯一的最大子解，我们caracerous。然后我们比较了隐障碍（2）和障碍：M+ u= k+ infess Ω <$0 x+<$∈ Ω <${c 0（k）+ u（x+<$）}，最后证明了在一般假设下，（1）的解是保持器连续的.
Abstract We study Quasi-Variational Inequalities:(1){Max (A u− f, u− M u)= 0, u|∂ Ω= φ, where (2) M u= k+ inf ξ≧ 0 x+ ξ∈ Ω¯{c 0 (ξ)+ u (x+ ξ)}. In general,(1) has no solution, we prove here that (1) has a unique maximum subsolution that we caracterize. Then we compare the implicit obstacle (2) and the obstacle: M+ u= k+ infess ξ≧ 0 x+ ξ∈ Ω¯{c 0 (ξ)+ u (x+ ξ)} and we finally show that, under general assumptions, the solution of (1) is Holder continuous.