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Keywords:
complex calculus of variation; Hamilton-Jacobi equations
complex calculus of variation; Hamilton-Jacobi equations
Summary:
In this article, we present a detailed study of the complex calculus of variations introduced in [M. Gondran: Calcul des variations complexe et solutions explicites d’équations d’Hamilton–Jacobi complexes. C.R. Acad. Sci., Paris 2001, t. 332, série I]. This calculus is analogous to the conventional calculus of variations, but is applied here to ${\mathbf{C}}^n$ functions in ${\mathbf{C}}$. 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.
References:
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