A convergence result on the second boundary value problem for parabolic equations

TL;DR

This paper proves a convergence result for a class of parabolic equations and uses it to demonstrate the existence of solutions for a specific boundary value problem involving special Lagrangian equations.

Contribution

It introduces a new convergence theorem and applies it to establish solutions for the second boundary value problem in special Lagrangian equations.

Findings

Established a Schnürer's convergence result for parabolic equations.

Proved existence of solutions for the second boundary value problem.

Applied the convergence result to special Lagrangian equations.

Abstract

We establish a Schn$\ddot{\text{u}}$rer's convergence result and then apply it to obtain the existence of solutions on the second boundary value problem for a family of special Lagrangian equations