Complex calculus of variations
In this article, we present a detailed study of the complex calculus of variations introduced in [4]. This calculus is analogous to the conventional calculus of variations, but is applied here to C-n functions in C. It is based on new concepts involving the minimum and convexity of a complex function. Such an approach allows us to propose explicit solutions to complex Hamilton-Jacobi equations, in particular by generalizing the Hopf-Lax formula.
complex calculus of variation hamilton-jacobi equations