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Sponsored AI Networking Cookbook: Practical recipes for AI-assisted network automation and development AI Networking Cookbook: Practical recipes for AI-assisted network automation and development

Author

Pierre Bousquet

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Preprint Sep 2026

Approximation in norm and energy with bounded functions for autonomous variational problems

We study the approximation of finite-energy Sobolev functions by bounded Sobolev functions for integral functionals associated with possibly signed Carath\'eodory integrands. The approximating sequence is required to converge strongly in the Sobolev space, while the corresponding energy densities converge in \(L^1\). O...

Pierre Bousquet, C. Mariconda, G. Treu · 0 citations
Preprint Sep 2026

Beyond Constant Truncations: The Bounded Sobolev Approximation Gap

We study the approximation of finite-energy Sobolev functions by bounded Sobolev functions for integral functionals associated with possibly signed Carath\'eodory integrands. The approximating sequence is required to converge strongly in the Sobolev space, while the corresponding energy densities converge in \(L^1\). O...

Pierre Bousquet, C. Mariconda, G. Treu · 1 citation

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