{"product_id":"partial-differential-equations-paperback-9780521277594","title":"Partial Differential Equations (Paperback) 9780521277594","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003ePartial Differential Equations\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThis book is a rigorous introduction to the abstract theory of partial differential equations.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJ. Wloka (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521277594, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 21 May 1987\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e532 pages\u003cbr\u003e22.7 x 15.1 x 3.4 cm, 0.774 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'The work under discussion is a nice presentation of PDEs and proves to be a valuable source for undergraduate and graduate students at all levels. It highlights the importance of studying di?erential equations both in the setting of classical solutions as well as weak solutions.' Marius Ghergu, European Mathematical Society\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis book is a rigorous introduction to the abstract theory of partial differential equations. The main prerequisite is familiarity with basic functional analysis: more advanced topics such as Fredholm operators, the Schauder fixed point theorem and Bochner integrals are introduced when needed, and the book begins by introducing the necessary material from the theory of distributions and Sobolev spaces. Using such techniques, the author presents different methods available for solving elliptic, parabolic and hyperbolic equations. He also considers the difference process for the practical solution of a partial differential equation, emphasising that it is possible to solve them numerically by simple methods. Many examples and exercises are provided throughout, and care is taken to explain difficult points. Advanced undergraduates and graduate students will appreciate this self-contained and practical introduction.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e Part I. Sobolev Spaces: 1. Notation, basic properties, distributions\u003cbr\u003e 2. Geometric assumptions for the domain\u003cbr\u003e 3. Definitions and density properties for the Sobolev-Slobodeckii spaces \u003cbr\u003e 4. The transformation theorem and Sobolev spaces on differentiable manifolds\u003cbr\u003e 5. Definition of Sobolev spaces by the Fourier transformation and extension theorems\u003cbr\u003e 6. Continuous embeddings and Sobolev's lemma\u003cbr\u003e 7. Compact embeddings\u003cbr\u003e 8. The trace operator\u003cbr\u003e 9. Weak sequential compactness and approximation of derivatives by difference quotients\u003cbr\u003e Part II. Elliptic Differential Operators: 10. Linear differential operators\u003cbr\u003e 11. The Lopatinskil-Sapiro condition and examples\u003cbr\u003e 12. Fredholm operators\u003cbr\u003e 13. The main theorem and some theorems on the index of elliptic boundary value problems\u003cbr\u003e 14. Green's formulae\u003cbr\u003e 15. The adjoint boundary value problem and the connection with the image space of the original operator\u003cbr\u003e 16. Examples\u003cbr\u003e Part III. Strongly Elliptic Differential Operators and the Method of Variations: 17. Gelfand triples, the Law-Milgram, V-elliptic and V-coercive operators\u003cbr\u003e 18. Agmon's condition\u003cbr\u003e 19. Agmon's theorem: conditions for the V-coercion of strongly elliptic differential operators\u003cbr\u003e 20. Regularity of the solutions of strongly elliptic equations\u003cbr\u003e 21. The solution theorem for strongly elliptic equations and examples\u003cbr\u003e 22. The Schauder fixed point theorem and a non-linear problem\u003cbr\u003e 23. Elliptic boundary value problemss for unbounded regions\u003cbr\u003e Part IV. Parabolic Differential Operators: 24. The Bochner integral\u003cbr\u003e 25. Distributions with values in a Hilbert space H and the space W\u003cbr\u003e 26. The existence and uniqueness of the solution of a parabolic differential equation\u003cbr\u003e 27. The regularity of solutions of the parabolic differential equation\u003cbr\u003e 28. Examples\u003cbr\u003e Part V. Hyperbolic Differential Operators: 29. Existence and uniqueness of the solution\u003cbr\u003e 30. Regularity of the solutions of the hyperbolic differential equation\u003cbr\u003e Part VI. Difference Processes for the Calculation of the Solution of the Partial Differential Equation: 32. Functional analytic concepts for difference processes\u003cbr\u003e 33. Difference processes for elliptic differential equations and for the wave equation\u003cbr\u003e 34. Evolution equations\u003cbr\u003e References\u003cbr\u003e Function and distribution spaces\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Integral calculus \u0026amp; equations [\u003ca title=\"See our other books on Integral calculus \u0026amp; equations\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Integral%20calculus%20\u0026amp;%20equations%20%5BPBKL%5D%22\"\u003ePBKL\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46006969958680,"sku":"9780521277594","price":65.88,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521277594i_7e3644a3-5383-4280-a756-478ba5d4ac86.jpg?v=1691374391","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/partial-differential-equations-paperback-9780521277594","provider":"Freshly Printed Books","version":"1.0","type":"link"}