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.
