Gevrey regularity of subelliptic Monge-Ampère equations in the plane

Hua Chen (1) , Weixi Li (1) , Chao-Jiang Xu (2)

1 School of Mathematics and Statistics [Wuhan]
2 LMRS - Laboratoire de Mathématiques Raphaël Salem

In this paper, we establish the Gevrey regularity of solutions for a class of degenerate Monge-Amp\'{e}re equations in the plane, under the assumption that one principle entry of the Hessian is strictly positive and an appropriately finite type degeneracy degeneracy, then we prove that the solution of the degenerate Monge-Amp'ere equation will be smooth in Gevrey classes.

Mots clés: Monge-Ampère equations; Gevrey regularity; subellipticity

Domaines: Equations aux dérivées partielles [math.AP]

Hua Chen, Weixi Li, Chao-Jiang Xu. Gevrey regularity of subelliptic Monge-Ampère equations in the plane. Advances in Mathematics, 2011, 228, pp.1816-1841. ⟨hal-00602976⟩