Gevrey regularity of subelliptic Monge-Amp\`ere equations in the plane

TL;DR

This paper proves that solutions to certain degenerate Monge-Ampère equations in the plane are Gevrey regular, assuming a positive principal Hessian entry and finite type degeneracy, advancing understanding of their smoothness properties.

Contribution

It establishes the Gevrey regularity of solutions for a class of degenerate Monge-Ampère equations under specific degeneracy and positivity conditions.

Findings

Solutions are Gevrey regular under given conditions

Regularity results apply to equations with finite type degeneracy

Advances understanding of smoothness in degenerate Monge-Ampère equations

Abstract

In this paper, we establish the Gevrey regularity of solutions for a class of degenerate Monge-Amp\`ere equations in the plane, under the assumption that one principle entry of the Hessian is strictly positive and an appropriately finite type degeneracy.