论文标题
关于在超季度汉密尔顿 - 雅各比方程中Höldereminorms的改善
On the improvement of Hölder seminorms in superquadratic Hamilton-Jacobi equations
论文作者
论文摘要
我们在本文中表明，与时间相关的粘性汉密尔顿 - 雅各比方程的最大$ l^q $ - 型号具有无限右侧的右侧和超级级别的$γ$ - 增长梯度的增长在整个范围内$ q>（n+2）\ frac {frac {γ-1}γ$。我们的方法基于新的$ \ frac {γ-2} {γ-1} $-Hölder估计，这是在适当的非线性空间和时间hölder商的小尺度上衰减的结果。这是通过证明合适的振荡估计值来获得的，这又为整个解决方案提供了一些Liouville类型的结果。
We show in this paper that maximal $L^q$-regularity for time-dependent viscous Hamilton-Jacobi equations with unbounded right-hand side and superquadratic $γ$-growth in the gradient holds in the full range $ q > (N+2)\frac{γ-1}γ$. Our approach is based on new $\frac{γ-2}{γ-1}$-Hölder estimates, which are consequence of the decay at small scales of suitable nonlinear space and time Hölder quotients. This is obtained by proving suitable oscillation estimates, that also give in turn some Liouville type results for entire solutions.
