In this paper we generalize an equation studied by Mossino and Temam in [7], to the fully nonlinear case. This equation arises in plasma physics as an approximation to Grad equations, which were introduced by Harold Grad in [4], to model the behavior of plasma confined in a toroidal vessel called TOKAMAK. We prove existence of a -viscosity solution and regularity up to for any (we improve this regularity near the boundary). The difficulty of this problem lies in the right-hand side which involves the measure of the superlevel sets, making the problem nonlocal. © 2021 Wiley Periodicals LLC.

中文翻译：

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完全非线性方程及其在等离子体物理学梯度方程中的应用

在本文中，我们将 Mossino 和 Temam 在 [7] 中研究的方程推广到完全非线性的情况。该方程作为 Grad 方程的近似值出现在等离子体物理学中，由 Harold Grad 在 [4] 中引入，用于模拟限制在称为托卡马克的环形容器中的等离子体行为。我们证明了 -粘度解的存在性和规律性（我们在边界附近改进了这种规律性）。该问题的难点在于右侧涉及超水平集的测度，使问题成为非局部问题。© 2021 Wiley Periodicals LLC。