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Fully Nonlinear Equations with Applications to Grad Equations in Plasma Physics
Communications on Pure and Applied Mathematics ( IF 3.1 ) Pub Date : 2021-11-08 , DOI: 10.1002/cpa.22026
Luis A. Caffarelli 1 , Ignacio Tomasetti 1
Affiliation  

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 urn:x-wiley:00103640:media:cpa22026:cpa22026-math-0001-viscosity solution and regularity up to urn:x-wiley:00103640:media:cpa22026:cpa22026-math-0002 for any urn:x-wiley:00103640:media:cpa22026:cpa22026-math-0003 (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:

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 -urn:x-wiley:00103640:media:cpa22026:cpa22026-math-0001粘度解的存在性和规律性urn:x-wiley:00103640:media:cpa22026:cpa22026-math-0002urn:x-wiley:00103640:media:cpa22026:cpa22026-math-0003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。
更新日期:2021-11-08
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