Nonlinear Functional Analysis and Its Applications: II/ A: Linear Monotone OperatorsSpringer Science & Business Media, 11 dic 1989 - 467 pagine This is the second of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self -contained and accessible to the nonspecialist. Part II concerns the theory of monotone operators. It is divided into two subvolumes, II/A and II/B, which form a unit. The present Part II/A is devoted to linear monotone operators. It serves as an elementary introduction to the modern functional analytic treatment of variational problems, integral equations, and partial differential equations of elliptic, parabolic and hyperbolic type. This book also represents an introduction to numerical functional analysis with applications to the Ritz method along with the method of finite elements, the Galerkin methods, and the difference method. Many exercises complement the text. The theory of monotone operators is closely related to Hilbert's rigorous justification of the Dirichlet principle, and to the 19th and 20th problems of Hilbert which he formulated in his famous Paris lecture in 1900, and which strongly influenced the development of analysis in the twentieth century. |
Sommario
III | 15 |
IV | 17 |
V | 19 |
VI | 21 |
VII | 28 |
VIII | 32 |
IX | 35 |
X | 40 |
LXII | 235 |
LXIII | 237 |
LXIV | 241 |
LXV | 251 |
LXVI | 253 |
LXVII | 255 |
LXVIII | 260 |
LXIX | 261 |
XI | 56 |
XII | 59 |
XIII | 60 |
XIV | 64 |
XV | 70 |
XVI | 71 |
XVII | 72 |
XVIII | 78 |
XIX | 79 |
XX | 81 |
XXI | 85 |
XXII | 86 |
XXIII | 93 |
XXIV | 101 |
XXV | 108 |
XXVI | 111 |
XXVII | 113 |
XXVIII | 115 |
XXIX | 116 |
XXX | 119 |
XXXI | 121 |
XXXII | 124 |
XXXIII | 126 |
XXXIV | 129 |
XXXV | 132 |
XXXVI | 134 |
XXXVII | 135 |
XXXVIII | 138 |
XXXIX | 141 |
XL | 143 |
XLI | 145 |
XLII | 153 |
XLIII | 155 |
XLIV | 159 |
XLV | 160 |
XLVI | 171 |
XLVIII | 174 |
XLIX | 175 |
L | 192 |
LI | 195 |
LII | 199 |
LIII | 200 |
LIV | 203 |
LV | 208 |
LVI | 210 |
LVII | 211 |
LVIII | 225 |
LIX | 229 |
LXI | 231 |
LXX | 262 |
LXXI | 265 |
LXXIII | 271 |
LXXIV | 273 |
LXXV | 275 |
LXXVI | 279 |
LXXVII | 283 |
LXXVIII | 285 |
LXXIX | 286 |
LXXX | 290 |
LXXXI | 292 |
LXXXII | 294 |
LXXXIII | 296 |
LXXXIV | 314 |
LXXXV | 320 |
LXXXVI | 325 |
LXXXVII | 335 |
LXXXVIII | 337 |
LXXXIX | 339 |
XC | 345 |
XCI | 347 |
XCII | 349 |
XCIII | 350 |
XCIV | 351 |
XCV | 352 |
XCVI | 357 |
XCVII | 361 |
XCVIII | 364 |
XCIX | 366 |
C | 369 |
CI | 371 |
CII | 374 |
CIII | 376 |
CIV | 378 |
CV | 383 |
CVI | 384 |
CVII | 402 |
CVIII | 406 |
CIX | 410 |
CX | 416 |
CXI | 417 |
CXII | 422 |
CXIII | 423 |
CXIV | 426 |
CXV | 430 |
CXVI | 452 |
CXVII | 453 |
CXIX | 456 |
CXX | 459 |
Altre edizioni - Visualizza tutto
Nonlinear Functional Analysis and Its Applications: II/ A: Linear Monotone ... E. Zeidler Anteprima limitata - 2012 |
Nonlinear Functional Analysis and its Applications: II/B: Nonlinear Monotone ... E. Zeidler Anteprima limitata - 2013 |
Nonlinear Functional Analysis and Its Applications: II/ A: Linear Monotone ... E. Zeidler Anteprima non disponibile - 1990 |
Parole e frasi comuni
Ad(a Assume H1 B-space bilinear boundary value problem bounded region C¹(G Chapter classical solution compact consider const constant convergence convex Corollary corresponding D(AF definition denote dense derivatives Dirichlet principle eigenvalue problem energetic space equivalent error estimates example exists finite elements following assumptions formula Friedrichs extension Galerkin equations Galerkin method Gårding inequality Hence Hilbert Hölder inequality implies L₂(G Lemma Let G Let u e linear operator linear subspace mathematical minimum problem monotone operators nonlinear norm obtain operator equation original problem orthogonal partial differential equations polynomials proof of Theorem real function real H-space region in RN resp Ritz equation Ritz method S₂ scalar product Section self-adjoint semigroup sequence Sobolev embedding theorems Sobolev spaces strongly monotone strongly positive Suppose symmetric u₁ ue D(A unique solution variational problem w₁ W₂(G yields
Brani popolari
Pagina 14 - ... when David Hilbert died in Gottingen on February the 14th, 1943, at the age of eightyone. In retrospect it seems to us that the era of mathematics upon which he impressed the seal of his spirit and which is now sinking below the horizon achieved a more perfect balance than prevailed before and after, between the mastering of single concrete problems and the formation of general abstract concepts. Hilbert's own work contributed not a little to bringing about this happy equilibrium, and the direction...
Pagina 14 - ... political, social, or spiritual, he stood forever on the side of freedom, frequently in isolated opposition against the compact majority of his environment.
Pagina 1 - ... understanding earlier theories and cast aside older more complicated developments. It is therefore possible for the individual investigator, when he makes these sharper tools and simpler methods his own, to find his way more easily in the various branches of mathematics than is possible in any other science. The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena.
Pagina 14 - ... was not afraid to swim against the current, even amidst the violent passions aroused by the first world war that swept so many other scientists off their feet. It was not mere chance that when the Nazis "purged" the German universities in 1933 their hand fell most heavily on the Hilbert school and that Hilbert's most intimate collaborators left Germany either voluntarily or under the pressure of Nazi persecution. He himself was too old, and stayed behind ; but the years after 1933 became for...