On diffeologies from infinite dimensional geometry to PDE constrained optimization
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Publication:6120740
DOI10.1090/conm/794/15938arXiv2302.07838OpenAlexW4391547868MaRDI QIDQ6120740
Kathrin Welker, Jean-Pierre Magnot, Unnamed Author
Publication date: 21 February 2024
Published in: Contemporary Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2302.07838
Applications of global analysis to the sciences (58Z05) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Infinite-dimensional manifolds (46T05)
Cites Work
- Diffeological vector pseudo-bundles
- Computational comparison of surface metrics for PDE constrained shape optimization
- A continuum mechanical approach to geodesics in shape space
- Sobolev metrics on shape space of surfaces
- The \(D\)-topology for diffeological spaces
- Diffeological gluing of vector pseudo-bundles and pseudo-metrics on them
- Scalable shape optimization methods for structured inverse modeling in 3D diffusive processes
- A Lie algebra for Frölicher groups
- On shape of plane elastic curves
- A metric on shape space with explicit geodesics
- Shape metrics based on elastic deformations
- The geometry of loop groups
- The diffeology of Milnor's classifying space
- The group of diffeomorphisms of a non-compact manifold is not regular
- Conservation laws and the variational bicomplex for second-order scalar hyperbolic equations in the plane
- Sobolev metrics on shape space. II: Weighted Sobolev metrics and almost local metrics
- Well-posedness of the Kadomtsev-Petviashvili hierarchy, Mulase factorization, and Frölicher Lie groups
- On the domain of implicit functions in a projective limit setting without additional norm estimates
- Simplicial cochain algebras for diffeological spaces
- Suitable spaces for shape optimization
- An exotic zoo of diffeomorphism groups on \(\mathbb {R}^n\)
- The homotopy theory of diffeological spaces
- An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach
- Riemannian geometries on spaces of plane curves
- Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms
- Model category of diffeological spaces
- Exterior bundles in diffeology
- Large-Scale Three-Dimensional Acoustic Horn Optimization
- AMBROSE–SINGER THEOREM ON DIFFEOLOGICAL BUNDLES AND COMPLETE INTEGRABILITY OF THE KP EQUATION
- THE SMOOTH STRUCTURE OF THE SPACE OF PIECEWISE-SMOOTH LOOPS
- Optimal Shape Design Subject to Elliptic Variational Inequalities
- Efficient PDE Constrained Shape Optimization Based on Steklov--Poincaré-Type Metrics
- A Nonlinear Elastic Shape Averaging Approach
- Geometry in a Fréchet Context
- Shape Optimization of an Electric Motor Subject to Nonlinear Magnetostatics
- Approximate Shape Gradients for Interface Problems
- Orbifolds as diffeologies
- Shape Manifolds, Procrustean Metrics, and Complex Projective Spaces
- Partial Differential Relations
- The inverse function theorem of Nash and Moser
- Iterated path integrals
- Sur L'Intégrabilité des Sous–Algèbres de lie en Dimension Infinie
- A Second Order Shape Optimization Approach for Image Segmentation
- DW Complexes and Their Underlying Topological Spaces
- SIKORSKI AND FRÖLICHER CW-COMPLEXES COMPARED
- A comparison between two de Rham complexes in diffeology
- Gauge Field Theory in Natural Geometric Language
- On the differential geometry of numerical schemes and weak solutions of functional equations
- Comparative Smootheology
- Diffeological Clifford algebras and pseudo-bundles of Clifford modules
- On tangent cones of Frölicher spaces
- The Geometry of Infinite-Dimensional Groups
- Groups of Diffeomorphisms and their Subgroups
- Tangent spaces and tangent bundles for diffeological spaces
- Laplace operators on differential forms over configuration spaces
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