Approximation for convex functionals on non-positively curved spaces and the Trotter–Kato product formula

DOI10.1515/acv.2011.011zbMath1245.47018OpenAlexW2334058012MaRDI QIDQ2883328

Igor Stojkovic

Publication date: 8 May 2012

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/acv.2011.011

zbMATH Keywords

CAT(0) spacesconvergence theoremsgradient flowscomparison geometryproduct formulasconvex functionalsapproximation semigroups

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) Fixed-point and coincidence theorems (topological aspects) (54H25) Metric geometry (51F99) Optimality conditions for free problems in two or more independent variables (49K10) Abstract integral equations, integral equations in abstract spaces (45N99)

Related Items

On the generation of nonlinear semigroups of contractions and evolution equations on Hadamard manifolds ⋮ A new proof of the Lie–Trotter–Kato formula in Hadamard spaces ⋮ Old and new challenges in Hadamard spaces ⋮ Existence, uniqueness and an ODE approach to the \(L^1\)-Karcher mean ⋮ Convergence of nonlinear semigroups under nonpositive curvature ⋮ Monotone Vector Fields and Generation of Nonexpansive Semigroups in Complete CAT(0) Spaces ⋮ The asymptotic behavior of a class of nonlinear semigroups in Hadamard spaces

Cites Work

• Contractions in the 2-Wasserstein length space and thermalization of granular media
• A concept of convergence in geodesic spaces
• The asymptotic behavior of a class of nonlinear semigroups in the Hilbert ball
• Trotter's product formula for nonlinear semigroups generated by the subdifferentials of convex functionals
• Equilibrium maps between metric spaces
• Cheeger type Sobolev spaces for metric space targets
• Nonlinear Markov operators, discrete heat flow, and harmonic maps between singular spaces
• A semigroup approach to harmonic maps
• Monotonicity, resolvents and Yosida approximations of operators on Hilbert manifolds.
• Nonlinear martingale theory for processes with values in metric spaces of nonpositive curvature
• Convex functionals and generalized harmonic maps into spaces of non positive curvature
• Differential and metrical structure of positive operators
• On \(\Delta\)-convergence theorems in CAT\((0)\) spaces
• Nonpositive curvature: A geometrical approach to Hilbert-Schmidt operators
• Sectional curvatures in nonlinear optimization
• Approximation of semi-groups of nonlinear operators
• Convergence and approximation of semigroups of nonlinear operators in Banach spaces
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• Nonexpansive iterations in hyperbolic spaces
• Open map theorem for metric spaces
• Gradient flows on Wasserstein spaces over compact Alexandrov spaces
• Monotone vector fields and the proximal point algorithm on Hadamard manifolds
• The Variational Formulation of the Fokker--Planck Equation
• Generation of Semi-Groups of Nonlinear Transformations on General Banach Spaces

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