Complex calculus of variations
Michel Gondran; Rita Hoblos Saade
Kybernetika (2003)
- Volume: 39, Issue: 2, page [249]-263
- ISSN: 0023-5954
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topGondran, Michel, and Saade, Rita Hoblos. "Complex calculus of variations." Kybernetika 39.2 (2003): [249]-263. <http://eudml.org/doc/33638>.
@article{Gondran2003,
abstract = {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.},
author = {Gondran, Michel, Saade, Rita Hoblos},
journal = {Kybernetika},
keywords = {complex calculus of variation; Hamilton-Jacobi equations; complex calculus of variation; Hamilton-Jacobi equations},
language = {eng},
number = {2},
pages = {[249]-263},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Complex calculus of variations},
url = {http://eudml.org/doc/33638},
volume = {39},
year = {2003},
}
TY - JOUR
AU - Gondran, Michel
AU - Saade, Rita Hoblos
TI - Complex calculus of variations
JO - Kybernetika
PY - 2003
PB - Institute of Information Theory and Automation AS CR
VL - 39
IS - 2
SP - [249]
EP - 263
AB - 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.
LA - eng
KW - complex calculus of variation; Hamilton-Jacobi equations; complex calculus of variation; Hamilton-Jacobi equations
UR - http://eudml.org/doc/33638
ER -
References
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- Gondran M., 10.1016/S0764-4442(01)01901-2, C.R. Acad. Sci., Paris 2001, t. 332, série I, pp. 677–680 Zbl1007.49014MR1842467DOI10.1016/S0764-4442(01)01901-2
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