{"product_id":"nonlinear-partial-differential-equations-in-geometry-and-physics-the-1995-barrett-lectures-9783764354930","title":"Nonlinear Partial Differential Equations in Geometry and Physics: The 1995 Barrett Lectures","description":"\u003cp\u003e • Author(s): Garth Baker\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Birkhauser\u003cbr\u003e • BISAC: Physics - Mathematical \u0026amp; Computational\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eNew Directions in 4-Manifold Theory.- Lecture 1: Donaldson and Seiberg-Witten Invariants.- Lecture 2: The Immersed Thorn Conjecture.- Lecture 3: Intersection Forms of Smooth 4-Manifolds.- References.- On the Regularity of Classical Field Theories in Minkowski Space-Time E3+1.- 1 Relativistic Field Theories.- 2 The Problem of Break-down.- 3 Energy estimates and the Problem of Optimal Local Well Posedness.- 4 Proof of the Null Estimates.- 5 The Proof of Theorem 4.- 6 Conclusions.- Static and Moving Vortices in Ginzburg-Landau Theories.- Lecture 1.- 1 Background and Models.- 2 The Work of Bethuel-Brézis-Hélein and Others.- 3 Some Generalizations.- Lecture 2.- 1 Renormalized Energy.- 2 A Technical Result.- 3 Proof of Theorem A.- 4 Proof of Theorem B.- Lecture 3: The Dynamical Law of Ginzburg-Landau Vortices.- 1 Gor'kov-Eliashberg's Equation.- 2 Uniqueness of Asymptotic Limit.- 3 Vortex Motion Equations.- References.- Wave Maps.- 1 Local existence. Energy method.- 1.1 The setting.- 1.2 Wave Maps.- 1.3 Examples.- 1.4 Basic questions.- 1.5 Energy estimates.- 1.6 L2-theory.- 1.7 Local existence for smooth data.- 1.8 A slight improvement.- 1.9 Global existence, the case m = 1.- 2 Blow-up and non-uniqueness.- 2.1 Overview.- 2.2 Regularity in the elliptic and parabolic cases.- 2.3 Regularity in the hyperbolic case.- 3 The conformai case m = 2.- 3.1 Overview.- 3.2 The equivariant case.- 3.3 Towards well-posedness for general targets.- 3.4 Approximation solutions.- 3.5 Convergence.- References.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Hardcover","offer_id":45282012856471,"sku":"9783764354930","price":5873.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783764354930.webp?v=1769300885","url":"https:\/\/atlanticbooks.com\/products\/nonlinear-partial-differential-equations-in-geometry-and-physics-the-1995-barrett-lectures-9783764354930","provider":"Atlantic Books","version":"1.0","type":"link"}