Tölle, Jonas M.: Variational convergence of nonlinear partial differential operators on varying Banach spaces. 2010
Inhalt
- Introduction
- Preliminaries
- Basic notations
- Bilinear forms and linear operators
- Monotone operators
- Convex functionals
- The subgradient
- Gâteaux and Fréchet differentiability
- The Legendre-Fenchel transform
- Infimal convolution and Moreau-Yosida approximation
- A variational setting
- Weighted Orlicz-Sobolev spaces
- H=W for weighted p-Sobolev spaces
- Muckenhoupt weights
- Weakly differentiable weights: A new condition for uniqueness
- The classical case recovered
- The general theory of varying Banach spaces
- Gromov-Hausdorff convergence
- Strong asymptotic relation
- Weak and weak asymptotic relation
- Metric approximation
- Strong convergence
- Weak and weak convergence
- Correspondence
- Asymptotic continuity
- Asymptotic reflexivity and weak compactness
- The asymptotic Kadec-Klee property
- Asymptotic embeddings
- A useful isometric result
- Overview
- Addendum: Asymptotic topology
- Examples of varying Banach spaces
- Hilbert spaces
- Lp-spaces
- Orlicz spaces
- Scales of Banach spaces
- Finite dimensional approximation
- Two-scale convergence
- Variational convergence of operators and forms
- Lifting via asymptotic isometry
- Convergence of bounded linear operators
- Convergence of bilinear forms
- G-convergence of nonlinear operators
- , Mosco and slice convergence
- G-convergence of subdifferentials
- Examples of Mosco and slice convergence
- Convergence of weighted -Laplace operators
- Convergence of weighted p-Laplace operators
- p1: The critical case
- Convergence of generalized porous medium and fast diffusion operators
- Facts from general topology
- The geometry of Banach spaces
- Convexity and smoothness
- Gauges and the duality map
- The Kadec-Klee property
- Schauder bases
- Orthogonality in Banach space
- Orlicz spaces
- Bibliography