[Lagrangiens autoconjugués non-convexes et principes variationnels associés à certaines EDP]
Nous étudions le concept des Lagrangiens autoconjugués non-convexes ainsi que le calcul qui leur est associé, de même que leurs champs de vecteurs derivés, reliés à nombre dʼéquations aux dérivées partielles et de systèmes dʼévolution. Nous obtenons de nouvelles formulations variationnelles pour une grande classe dʼéquations aux dérivées partielles et comprenant une large variété de conditions aux limites linéaires et non-linéaires qui englobe la plupart des conditions aux limites usuelles. Cette approche semble offrir certains avantages : Elle associe au problème aux limites donné un certain nombre de fonctions potentiel qui peuvent être maniées avec plus de facilité par rapport à dʼautres méthodes telles celles faisant usage des fonctions dʼEuler–Lagrange. Ces fonctions potentiel peuvent être aisément adaptées afin de traiter des problèmes aux limites non-linéaires et homogènes.
We study the concept and the calculus of non-convex self-dual (Nc-SD) Lagrangians and their derived vector fields which are associated to many partial differential equations and evolution systems. They yield new variational resolutions for large class of partial differential equations with variety of linear and non-linear boundary conditions including many of the standard ones. This approach seems to offer several useful advantages: It associates to a boundary value problem several potential functions which can often be used with relative ease compared to other methods such as the use of Euler–Lagrange functions. These potential functions are quite flexible, and can be adapted to easily deal with both non-linear and homogeneous boundary value problems.
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@article{CRMATH_2011__349_7-8_417_0,
author = {Moameni, Abbas},
title = {Non-convex self-dual {Lagrangians} and variational principles for certain {PDE's}},
journal = {Comptes Rendus. Math\'ematique},
pages = {417--420},
publisher = {Elsevier},
volume = {349},
number = {7-8},
year = {2011},
doi = {10.1016/j.crma.2011.01.028},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.01.028/}
}
TY - JOUR AU - Moameni, Abbas TI - Non-convex self-dual Lagrangians and variational principles for certain PDEʼs JO - Comptes Rendus. Mathématique PY - 2011 SP - 417 EP - 420 VL - 349 IS - 7-8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.01.028/ DO - 10.1016/j.crma.2011.01.028 LA - en ID - CRMATH_2011__349_7-8_417_0 ER -
%0 Journal Article %A Moameni, Abbas %T Non-convex self-dual Lagrangians and variational principles for certain PDEʼs %J Comptes Rendus. Mathématique %D 2011 %P 417-420 %V 349 %N 7-8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.01.028/ %R 10.1016/j.crma.2011.01.028 %G en %F CRMATH_2011__349_7-8_417_0
Moameni, Abbas. Non-convex self-dual Lagrangians and variational principles for certain PDEʼs. Comptes Rendus. Mathématique, Tome 349 (2011) no. 7-8, pp. 417-420. doi : 10.1016/j.crma.2011.01.028. http://www.numdam.org/articles/10.1016/j.crma.2011.01.028/
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