Anti-selfdual Lagrangians: Variational resolutions of non self-adjoint equations and dissipative evolutions
| dc.creator | Ghoussoub, Nassif | |
| dc.date | 2005-03-24 | |
| dc.date.accessioned | 2026-07-07T05:18:26Z | |
| dc.date.available | 2026-07-07T05:18:26Z | |
| dc.description | We develop the concept and the calculus of anti-self dual (ASD) Lagrangians which seems inherent to many questions in mathematical physics, geometry, and differential equations. They are natural extensions of gradients of convex functions --hence of self-adjoint positive operators-- which usually drive dissipative systems, but also rich enough to provide representations for the superposition of such gradients with skew-symmetric operators which normally generate unitary flows. They yield variational formulations and resolutions for large classes of non-potential boundary value problems and initial-value parabolic equations. Solutions are minima of functionals of the form $I(u)=L(u, Λu)$ (resp. $I(u)=\int_{0}^{T}L(t, u(t), \dot u (t)+Λ_{t}u(t))dt$) where $L$ is an anti-self dual Lagrangian and where $Λ_{t}$ are essentially skew-adjoint operators. However, and just like the self (and antiself) dual equations of quantum field theory (e.g. Yang-Mills) the equations associated to such minima are not derived from the fact they are critical points of the functional $I$, but because they are also zeroes of the Lagrangian $L$ itself. | |
| dc.description | 50 pages. For the most updated version of this paper, please visit http://www.pims.math.ca/~nassif/pims_papers.html | |
| dc.identifier | https://arxiv.org/abs/math/0503571 | |
| dc.identifier | http://arxiv.org/abs/math/0503571 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74658 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Anti-selfdual Lagrangians: Variational resolutions of non self-adjoint equations and dissipative evolutions | |
| dc.type | text |