Monge-Ampère Equation and Its Numerical Analysis

Abstract

In this study, we focus on the Monge-Amp` ere equation and its applications in non linear partial differential equations (PDEs). The work extends upon existing math ematical frameworks to include the derivation of the Monge-Amp`ere equation and its numerical solution. Employing a rigorous analytical approach, the derivation highlights the intrinsic geometric and variational principles underlying the equa tion. Furthermore, in the numerical solution, we use finite element techniques, implementing them to solve the Monge-Amp` ere equation efficiently using FEniCS.