Differentiability of Inverse Operators

DOI10.1007/978-3-319-00125-8_14zbMath1275.58004OpenAlexW154314707MaRDI QIDQ2845713

S. Ya. Serovaiskii

Publication date: 3 September 2013

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-00125-8_14

zbMATH Keywords

nonlinear elliptic equationnecessary conditions of optimalityinverse function theoremextended derivativeoperator derivative

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Nonlinear elliptic equations (35J60) Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20) Continuous and differentiable maps in nonlinear functional analysis (46T20)

Cites Work

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• High order inverse function theorems
• On inverse function theorems for set-valued maps
• Differentiation of inverse functions in spaces without norm.
• Optimization and nonsmooth analysis
• Analytic Proofs of the "Hairy Ball Theorem" and the Brouwer Fixed Point Theorem
• Calculation of functional gradients and extended differentiation of operators
• Local inversion theorems without assuming continuous differentiability
• Local inversion theorems without assuming continuous differentiability

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