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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Self-Dual Partial Differential Systems and Their Variational Principles

Self-Dual Partial Differential Systems and Their Variational Principles

Ghoussoub, Nassif

Hardcover

Series: Springer Monographs in Mathematics

Business GeneralGeneral Mathematics

ISBN10: 0387848967
ISBN13: 9780387848969
Publisher: Springer Nature
Published: Nov 11 2008
Pages: 354
Weight: 1.40
Height: 0.80 Width: 6.10 Depth: 9.30
Language: English
How to solve partial differential systems by completing the square. This could well have been the title of this monograph as it grew into a project to develop a s- tematic approach for associating suitable nonnegative energy functionals to a large class of partial differential equations (PDEs) and evolutionary systems. The minima of these functionals are to be the solutions we seek, not because they are critical points (i. e., from the corresponding Euler-Lagrange equations) but from also - ing zeros of these functionals. The approach can be traced back to Bogomolnyi's trick of completing squares in the basic equations of quantum eld theory (e. g., Yang-Mills, Seiberg-Witten, Ginzburg-Landau, etc., ), which allows for the deri- tion of the so-called self (or antiself) dual version of these equations. In reality, the self-dual Lagrangians we consider here were inspired by a variational - proach proposed - over 30 years ago - by Brezis and Ekeland for the heat equation and other gradient ows of convex energies. It is based on Fenchel-Legendre - ality and can be used on any convex functional - not just quadratic ones - making them applicable in a wide range of problems. In retrospect, we realized that the - ergy identities satis ed by Leray's solutions for the Navier-Stokes equations are also another manifestation of the concept of self-duality in the context of evolution equations.

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