论文标题
完全非线性方程，并在等离子体物理学的毕业方程中应用
Fully Nonlinear Equations with Applications to Grad Equations in Plasma Physics
论文作者
论文摘要
在本文中，我们将Mossino和Temam研究的方程式推广到完全非线性的情况下。该方程式是在血浆物理学中作为对毕业方程的近似值（由Harold Grad引入的），以模拟限制在环形血管中的血浆的行为。我们证明，对于任何$α<1 $，我们证明存在$ w^{2，p} $ - 粘度解决方案和规律性最高可达$ c^{1，α}（\OverlineΩ）$（我们在边界附近改善了此规律性）。这个问题的困难位于右侧，涉及超级高级集合的度量，这使得问题非本地。
In this paper we generalize an equation studied by Mossino and Temam, to the fully nonlinear case. This equation arises in plasma physics as an approximation to Grad equations, which were introduced by Harold Grad, to model the behavior of plasma confined in a toroidal vessel. We prove existence of a $W^{2,p}$-viscosity solution and regularity up to $C^{1,α}(\overlineΩ)$ for any $α<1$(we improve this regularity near the boundary). The difficulty of this problem lays on a right hand side which involves the measure of the superlevel sets, making the problem nonlocal.
