论文标题
血浆物理中产生的自由边界问题的新通用估计
New universal estimates for free boundary problems arising in plasma physics
论文作者
论文摘要
对于$ω\ subset \ mathbb {r}^2 $一个平滑且有界的域，我们得出了在等离子物理学中引起的$ω$的非阴性解决方案的急剧通用能量估计。结果，我们能够针对此类问题推断出新的通用估计。我们首先提出了一个尖锐的积极阈值，该阈值可以保证$ω$内部没有自由边界，或者同等地，对于$ω$的内部存在自由边界的必要条件。然后，我们得出了针对非负解的$ l^{\ infty} $的明确绑定的，并且还获得了相对于其他整齐密度边界值的阈值的显式估计。至少据我们所知，这些是超线性案例中此类的第一个明确估计。
For $Ω\subset \mathbb{R}^2$ a smooth and bounded domain, we derive a sharp universal energy estimate for non-negative solutions of free boundary problems on $Ω$ arising in plasma physics. As a consequence, we are able to deduce new universal estimates for this class of problems. We first come up with a sharp positivity threshold which guarantees that there is no free boundary inside $Ω$ or either, equivalently, with a sharp necessary condition for the existence of a free boundary in the interior of $Ω$. Then we derive an explicit bound for the $L^{\infty}$-norm of non-negative solutions and also obtain explicit estimates for the thresholds relative to other neat density boundary values. At least to our knowledge, these are the first explicit estimates of this sort in the superlinear case.
