Partial subdifferentials, derivates and Rademacher’s Theorem

DOI10.1090/S0002-9947-99-02203-5zbMath0924.49013OpenAlexW1507070361MaRDI QIDQ4243631

D. N. Bessis, Frank H. Clarke

Publication date: 19 May 1999

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-99-02203-5

zbMATH Keywords

nonsmooth analysislocally Lipschitz functionsGâteaux and Fréchet derivativesdirectional derivatespartial subdifferentialsstaunch sets

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Fréchet and Gateaux differentiability in optimization (49J50) Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20) Derivatives of functions in infinite-dimensional spaces (46G05)

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Cites Work

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• Convex functions, monotone operators and differentiability.
• Differentiability of Lipschitz functions on Banach spaces
• Fine topology methods in real analysis and potential theory
• Contrôle dans les inéquations variationelles elliptiques
• Gaussian null sets and differentiability of Lipschitz map on Banach spaces
• Choquet theorem and nonsmooth analysis
• Proximal analysis and minimization principles
• Proximal Analysis and Boundaries of Closed Sets in Banach Space. Part II: Applications
• A simple proof of the Rademacher theorem
• On Intermediate Differentiability of Lipschitz Functions on Certain Banach Spaces
• Generalized Gradients and Applications
• Sets of $\sigma$-porosity and sets of $\sigma $-porosity $(q)$
• Differentiability of Lipschitzian mappings between Banach spaces
• Differentiation of Real Functions
• Locally Lipschitz functions are generically pseudo-regular on separable Banach spaces

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