Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Third EditionHilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Rad??. The book gives a concise introduction to variational methods and presents an overview of areas of current research in the field. The third edition gives a survey on new developments in the field. References have been updated and a small number of mistakes have been rectified. |
Contents
Chapter I | 1 |
Chapter II | 74 |
E | 76 |
E | 144 |
Chapter III | 169 |
llull A | 180 |
о | 222 |
Appendix A | 237 |
Appendix B | 242 |
References | 251 |
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Variational Methods: Applications to Nonlinear Partial Differential ... Michael Struwe Limited preview - 2012 |
Common terms and phrases
applications assume assumption Banach space bounded domain C¹(V calculus of variations choose coercive conformal constant continuous convergence convex critical points curvature DE(u define denote differential Dirichlet dx dt E(um E(uo eigenvalue embedding energy estimate Euler-Lagrange equations exists finite function H¹¹² H¹¹²(N Hamiltonian systems harmonic map Hence Hölder's inequality holds homeomorphism homotopy inf sup integral invariant lim inf Lipschitz Lipschitz continuous lower semi-continuous manifold Math maximum principle mean curvature methods metric minimizing sequence Moreover neighborhood nonlinear norm Note obtain Palais-Smale condition particular periodic solutions Plateau problem proof of Theorem pseudo-gradient flow pseudo-gradient vector field Rabinowitz relative minimizer satisfies P.-S scalar scalar curvature Section semilinear elliptic smooth Sobolev solves Struwe Suppose symmetric Theorem 3.4 theory topology u₁ variational problem vector field Vul² weak weakly lower semi-continuous
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Page 262 - Metric critical point theory I. Morse regularity and homotopic stability of a minimum, J. Math. Pures Appl.
Page 269 - Steffen, K., On the existence of surfaces with prescribed mean curvature and boundary, Math. z. 146, 113-135 (1976).
Page 271 - A general existence theorem for surfaces of constant mean curvature. Math. Z. 120 (1971) 277-288 [3] The Dirichlet problem with a volume constraint.