论文标题
部分可观测时空混沌系统的无模型预测
Sharp regularity for singular obstacle problems
论文作者
论文摘要
我们获得了尖锐的本地$ c^{1，α} $针对单数障碍问题的规律性解决方案，Euler-lagrange方程式由此给出 $$ Δ_pu =γ（u-φ）^{γ-1} \，\ text {in} \，\ {u>φ\}， $$ 以$ 0 <γ<1 $和$ p \ ge2 $。在自由边界$ \ partial \ {u>φ\} $上，我们证明了最佳$ c^{1，τ} $定期解决方案，$τ$以$ p $，$γ$和$ $ $ $ $ $ $ $的$τ$，即使在线性设置中也是新的。
We obtain sharp local $C^{1,α}$ regularity of solutions for singular obstacle problems, Euler-Lagrange equation of which is given by $$ Δ_p u=γ(u-φ)^{γ-1}\,\text{ in }\,\{u>φ\}, $$ for $0<γ<1$ and $p\ge2$. At the free boundary $\partial\{u>φ\}$, we prove optimal $C^{1,τ}$ regularity of solutions, with $τ$ given explicitly in terms of $p$, $γ$ and smoothness of $φ$, which is new even in the linear setting.
