Partial Differential Equations: Second Edition (Graduate Studies in Mathematics) 2nd Edition by Lawrence C. Evans (PDF)

Description

This is the second edition of the now definitive text on partial differential equations (PDE). It offers a comprehensive survey of modern techniques in the theoretical study of PDE with particular emphasis on nonlinear equations. Its wide scope and clear exposition make it a great text for a graduate course in PDE. For this edition, the author has made numerous changes, including a new chapter on nonlinear wave equations, more than 80 new exercises, several new sections, a significantly expanded bibliography.

User’s Reviews

Editorial Reviews: Review I have used this book for both regular PDE and topics courses. It has a wonderful combination of insight and technical detail. … Evans’ book is evidence of his mastering of the field and the clarity of presentation. –Luis Caffarelli, University of TexasIt is fun to teach from Evans’ book. It explains many of the essential ideas and techniques of partial differential equations … Every graduate student in analysis should read it. –David Jerison, MITEvans’ book has already attained the status of a classic. It is a clear choice for students just learning the subject, as well as for experts who wish to broaden their knowledge … An outstanding reference for many aspects of the field. –Rafe Mazzeo, Stanford University

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a very clearly written, highly focused text on the basics (existence, uniqueness and regularity) of PDEs, with a really nice, simple and pragmatic approach to functional analysis. Hence, I believe that, at least with respect to linear DEs, this book is extremely helpful for building a satisfactory background for applied math and physics, for the pre-1960s world. In addition, the presentation of some simple exact results for the nonlinear theory is useful. Of course, the pure math specialist will want to delve far more deeply into the theory, but for an applied mathematician like myself (who struggled a lot just to get through Rudin’s basic books on real and complex analysis and functional analysis), this book gives a window into modern physics. Even for a Villani, who was obviously great at applied math in this area, I think Evans’ treatment, although a little pedestrian for a genius like that, would be helpful. There are a number of deficiencies, relative to the physicist’s point of view. There is not nearly a satisfactory treatment of the relationship of differential geometry to PDEs, and a physicist really needs the geometric perspective. In addition, Evans squanders a lot of his efforts on the pure math perspective (which can be helpful for the Villanis) for nonlinear theory, but the physicist requires a really good perspective on numerical PDEs. Finally, physicists have taken PDEs into quantum field theory and string theory, and other areas (such as stat mech where Villani worked), and there are numerous ideas developed in those areas, for example by Kenneth Wilson, Steven Weinberg, and the great string theorists, that need to be addressed to be helpful for a physicist not going into a classical area (fluid mechanics, classical electrodynamics, stat mech with Boltzmann’s equation, kinetic theory, etc.). But, Evans’ book is a great step on the road to the modern world, where we seem to be at the edge of significant advances beyond those major advances in physics and math from 1890 to about 1960 which has pretty much driven everything since then. I see a very steep climb beyond Evans to get to modern physics, much easier for a young person, than a retired older one like I am. Still, this is a step to the leading edge of today, where there are enormous potentials for advances (but of course, impossible to say whether they will be realized, but it seems pretty clear we are going to see some significant stuff coming in AI). It is the young who can open this door to the future, but even for an old guy like me, Evans’ book is a real plus for progress in understanding and gaining perspective.

⭐A real math book for grownups! Authoritative and comprehensive!

⭐An extremely good book for learning Partial Differential equations in a deeper analytic fashion. You’re going to want a beginners course in PDEs before tackling this book, as it’s focus is much more analytical, than brute force finding solutions.

⭐First of all, this is not a book for a first course in PDE’s. It requires prior knowledge of Functional Analysis and other disciplines of analysis which are not obtained in standard undergraduate courses. I agree with Professor Carlos Kenig, who says that suggests this book for his students before their first exam during the doctorate. In my opinion, it could have more motivation before the proofs or the introduction of a certain concepts. I like the new chapter about nonlinear wave equation.

⭐Evans is excellent at PDE and also has good pieces of aspects of analysis coming through.

⭐The boik is in great condition when it came to my mail.

⭐Genial..llegó a tiempo y en exelentes condiciones

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⭐This is the Great Book for Partial Differential Equations

⭐Great book on this topic – especially for graduate students. Professor Evans really comes straight to the point and all derivations and proofs contain the essential steps necessary. One does not need to do pages and pages of side calculations to come from one line to the next as in many other text books. No phrases “It is easy to see…” or “One obtains immediately…”. Thank you Professor Evans!

⭐Testo eccellente, ricco di argomenti interessanti, tra cui:- Soluzioni di PDE lineari: equazione del Trasporto, Poisson, Diffusione e Onde- Metodi per le PDE nonlineari, inclusa l’equazione di Hamilton-Jacobi- Esistenza e unicità per problemi con operatori differenziali ellittici- Problemi di minimizzazioneIn alcune occasioni risulta dispersivo per le troppo lunghe dimostrazioni, potrebbero essere riportate in appendici.Vi è una comodissima e ben fatta appendice di analisi funzionale che include una utile dimostrazione del teorema spettrale per operatori compatti ( anche in spazi a dimensioni non finite).Adatto a studenti di Matematica e a ingegneri e fisici intenzionati a migliorare le proprie competenze matematiche.

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⭐Ho acquistato questo libro per un personale approfondimento in questa materia (non frequento la facoltà di matematica) dato che mi trovo spesso ad affrontare a livello pratico problemi attraverso lo sviluppo di PDE’s. Infatti, anche se il testo è per me comprensibile, spazia in molti aspetti che personalmente non interessano.A mio parere il vantaggio di tale testo è la praticità: la maggior parte degli argomenti trattati a livello teorico sono seguiti da esempi applicativi che ne rendono immediato il campo di utilizzo e la comprensione. A mio parere è consigliato per chi vuole avere un buon riferimento per un argomento matematico particolare, altrimenti è meglio indirizzarsi verso testi più generici.Il testo è così sviluppato:Cap.1 : IntroductionPART 1 : REPRESENTATION FORMULAS FOR SOLUTIONSCap.2 : Four important linear PDECap.3 : Non-linear first order PDECap.4 : Other ways to represent solutionsPART 2 : THEORY FOR LINEAR PDECap.5 : Sobolev spacesCap.6 : Second order elliptical PDECap.7 : Linear evolution equationsPART 3 : THEORY FOR NONLINEAR PDECap.8 : The calculus of variationCap.9 : Nonvariational techniquesCap.10 : Hamilton-Jacobi equationsCap.11 : Systems of conservation lawsCap.12 : Nonlinear wave equationsAPPENDICESUnica pecca non riguarda il contenuto ma le condizioni di come è arrivato dato che sulla copertina posteriore era graffiato. Nulla di preoccupante (per chi non è pignolo).

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⭐This book provides a complete source of the basic topics of PDEs, presenting clear results and proofs. Of course, it can be used by students to prepare an exam of PDSs as well as by professors as a guideline for their lectures.

⭐Excelente libro para aprender sobre las EDPs, muy buenas explicaciones, lo recomiendo bastante. Y me vino nuevo en plástico envuelto.

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