{"product_id":"self-dual-partial-differential-systems-and-their-variational-principles-von-nassif-ghoussoub","title":"Self-dual Partial Differential Systems and Their Variational Principles","description":"\u003cp\u003eHow 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.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9781441927446\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9781441927446","offer_id":39415118168157,"sku":"9781441927446","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/bc63d4b2-a5e3-4413-aeeb-2b2be20d8648.jpg?v=1772169102","url":"https:\/\/shop.autorenwelt.de\/products\/self-dual-partial-differential-systems-and-their-variational-principles-von-nassif-ghoussoub","provider":"Autorenwelt Shop","version":"1.0","type":"link"}