04631nam a22004815i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001600153072001600169072002300185082001200208100002900220245007900249250002000328264004600348300004400394336002600438337002600464338003600490347002400526490005300550505082400603520224501427650001703672650002703689650002803716650003603744650001303780650001703793650001403810650005703824650003603881650004103917710003403958773002003992776003604012830005304048856004804101978-0-387-49319-0DE-He21320180115171409.0cr nn 008mamaa100429s2007 xxu| s |||| 0|eng d a97803874931907 a10.1007/978-0-387-49319-02doi 4aQA299.6-433 7aPBK2bicssc 7aMAT0340002bisacsh04a5152231 aJost, Jürgen.eauthor.10aPartial Differential Equationsh[electronic resource] /cby Jürgen Jost. aSecond Edition. 1aNew York, NY :bSpringer New York,c2007. aXIV, 356 p. 10 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aGraduate Texts in Mathematics,x0072-5285 ;v2140 aIntroduction: What Are Partial Differential Equations? -- The Laplace Equation as the Prototype of an Elliptic Partial Differential Equation of Second Order -- The Maximum Principle -- Existence Techniques I: Methods Based on the Maximum Principle -- Existence Techniques II: Parabolic Methods. The Heat Equation -- Reaction-Diffusion Equations and Systems -- The Wave Equation and its Connections with the Laplace and Heat Equations -- The Heat Equation, Semigroups, and Brownian Motion -- The Dirichlet Principle. Variational Methods for the Solution of PDEs (Existence Techniques III) -- Sobolev Spaces and L2 Regularity Theory -- Strong Solutions -- The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV) -- The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash. aThis book is intended for students who wish to get an introduction to the theory of partial differential equations. The author focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. These are maximum principle methods (particularly important for numerical analysis schemes), parabolic equations, variational methods, and continuity methods. This book also develops the main methods for obtaining estimates for solutions of elliptic equations: Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. Connections between elliptic, parabolic, and hyperbolic equations are explored, as well as the connection with Brownian motion and semigroups. This book can be utilized for a one-year course on partial differential equations. For the new edition the author has added a new chapter on reaction-diffusion equations and systems. There is also new material on Neumann boundary value problems, Poincaré inequalities, expansions, as well as a new proof of the Hölder regularity of solutions of the Poisson equation. Jürgen Jost is Co-Director of the Max Planck Institute for Mathematics in the Sciences and Professor of Mathematics at the University of Leipzig. He is the author of a number of Springer books, including Dynamical Systems (2005), Postmodern Analysis (3rd ed. 2005, also translated into Japanese), Compact Riemann Surfaces (3rd ed. 2006) and Riemannian Geometry and Geometric Analysis (4th ed., 2005). The present book is an expanded translation of the original German version, Partielle Differentialgleichungen (1998). About the first edition: Because of the nice global presentation, I recommend this book to students and young researchers who need the now classical properties of these second-order partial differential equations. Teachers will also find in this textbook the basis of an introductory course on second-order partial differential equations. - Alain Brillard, Mathematical Reviews Beautifully written and superbly well-organised, I strongly recommend this book to anyone seeking a stylish, balanced, up-to-date survey of this central area of mathematics. - Nick Lord, The Mathematical Gazette. 0aMathematics. 0aMathematical analysis. 0aAnalysis (Mathematics). 0aPartial differential equations. 0aPhysics.14aMathematics.24aAnalysis.24aTheoretical, Mathematical and Computational Physics.24aPartial Differential Equations.24aNumerical and Computational Physics.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780387493183 0aGraduate Texts in Mathematics,x0072-5285 ;v21440uhttp://dx.doi.org/10.1007/978-0-387-49319-0