# Partial Differential Equations

Springer Science & Business Media, Aug 12, 2002 - Mathematics - 325 pages
This textbook is intended for students who wish to obtain an introduction to the theory of partial di?erential equations (PDEs, for short), in particular, those of elliptic type. Thus, it does not o?er a comprehensive overview of the whole ?eld of PDEs, but tries to lead the reader to the most important methods and central results in the case of elliptic PDEs. The guiding qu- tion is how one can ?nd a solution of such a PDE. Such a solution will, of course, depend on given constraints and, in turn, if the constraints are of the appropriate type, be uniquely determined by them. We shall pursue a number of strategies for ?nding a solution of a PDE; they can be informally characterized as follows: (0) Write down an explicit formula for the solution in terms of the given data (constraints). This may seem like the best and most natural approach, but this is possible only in rather particular and special cases. Also, such a formula may be rather complicated, so that it is not very helpful for detecting qualitative properties of a solution. Therefore, mathematical analysis has developed other, more powerful, approaches. (1) Solve a sequence of auxiliary problems that approximate the given one, and show that their solutions converge to a solution of that original pr- lem. Di?erential equations are posed in spaces of functions, and those spaces are of in?nite dimension.

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### Contents

 III 7 IV 15 V 31 VII 37 VIII 42 IX 51 X 60 XI 64
 XXVI 172 XXVII 175 XXVIII 183 XXIX 193 XXX 208 XXXI 215 XXXII 223 XXXIII 229

 XII 69 XIII 77 XIV 87 XV 94 XVI 108 XVII 113 XVIII 117 XIX 121 XX 127 XXI 129 XXII 145 XXIII 157 XXIV 160 XXV 170
 XXXIV 243 XXXV 248 XXXVI 255 XXXVII 263 XXXVIII 269 XXXIX 275 XL 287 XLI 291 XLII 309 XLIII 317 XLIV 319 XLV 323 Copyright

### References to this book

 Mathematik für Physiker, Volume 2No preview available - 2004
 Compact Riemann Surfaces: An Introduction to Contemporary MathematicsJürgen JostLimited preview - 2006
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