Self-dual Partial Differential Systems and Their Variational PrinciplesSpringer Science & Business Media, 11.11.2008 - 354 Seiten This text is intended for a beginning graduate course on convexity methods for PDEs. The generality chosen by the author puts this under the classification of "functional analysis". The book contains new results and plenty of examples and exercises. |
Inhalt
Preface | 1 |
SELFDUAL SYSTEMS AND THEIR ANTISYMMETRIC | 12 |
Selfdual Lagrangians on Phase Space | 49 |
4 | 63 |
5 | 80 |
Variational Principles for Completely Selfdual Functionals | 99 |
Semigroups of Contractions Associated to Selfdual Lagrangians 119 | 118 |
Iteration of Selfdual Lagrangians and Multiparameter Evolutions | 147 |
The Class of Antisymmetric Hamiltonians 205 | 204 |
Variational Principles for Selfdual Functionals and First | 217 |
The Role of the CoHamiltonian in Selfdual Variational Problems 241 | 240 |
Direct Sum of Selfdual Functionals and Hamiltonian Systems | 253 |
Superposition of Interacting Selfdual Functionals 275 | 274 |
Hamiltonian Systems of Partial Differential Equations | 287 |
The Selfdual PalaisSmale Condition for Noncoercive Functionals | 305 |
NavierStokes and other Selfdual Nonlinear Evolutions 319 | 318 |
Direct Sum of Completely Selfdual Functionals 175 | 174 |
Semilinear Evolution Equations with Selfdual Boundary | 187 |
Andere Ausgaben - Alle anzeigen
Self-dual Partial Differential Systems and Their Variational Principles Nassif Ghoussoub Eingeschränkte Leseprobe - 2008 |
Self-dual Partial Differential Systems and Their Variational Principles Nassif Ghoussoub Keine Leseprobe verfügbar - 2010 |
Häufige Begriffe und Wortgruppen
Assume attained automorphism B-self-dual boundary conditions boundary Lagrangian boundary operator bounded linear operator boundedness Bv(T coercivity condition completely self-dual functional consider convex and lower convex function convex lower semicontinuous Corollary Dom₁ domain D(T dual duality evolution equations evolution triple exists formula function on H functional I(u Ghoussoub grangian H₁ Hamiltonian systems Hilbert space inf L(x infimum L²(Q Legendre transform Lemma lower semicontinuous function Lsd X;B maximal monotone operators minimizing monotone operators nonlinear norm obtain operator à path space PDEs phase space po(t problem Proof Proposition reflexive Banach space resp satisfies self-dual Lagrangian self-dual vector fields skew-adjoint modulo skew-adjoint operator solution space H Springer Science+Business Media subdifferential sup sup time-dependent self-dual Lagrangian uniformly convex variational principle variational resolution vector field X₁ Xp,q zero ди дх