July 29, 2024Archive for Rational Mechanics and AnalysisOpen Access

Quantified Legendreness and the Regularity of Minima

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CFCristiana De FilippisUniversity of Parma LKLukas KochUniversity of Sussex JKJan KristensenUniversity of Oxford

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Implication

Mathematical analysis reveals higher differentiability and smoothness for vector-valued minimizers of degenerate functionals, highlighting optimal regularity bounds for anisotropic polynomials.

Key Points

Higher differentiability and improved smoothness hold for vector-valued minimizers of degenerate functionals under quantified legendreness conditions.
Analysis using convex duality establishes higher differentiability bounds for nonuniformly elliptic variational problems without requiring standard growth.
Supports sharper regularity theory and extends to convex anisotropic polynomials, achieving an essentially optimal improvement over classical 1989 results.

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Filippis et al. (2024) studied this question.

synapsesocial.com/papers/68e5ea33b6db64358757ec52 https://doi.org/10.1007/s00205-024-02008-5

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Implication

Mathematical analysis reveals higher differentiability and smoothness for vector-valued minimizers of degenerate functionals, highlighting optimal regularity bounds for anisotropic polynomials.

Quantified Legendreness and the Regularity of Minima

Discussion

Member takes

Implication

Key Points

Cite This Study

Quantified Legendreness and the Regularity of Minima

Discussion

Member takes

Implication

Key Points

Cite This Study

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