Variational properties of local functionals driven by arbitrary anisotropies

Simone Verzellesi; Simone Verzellesi

doi:10.1007/s00526-025-03176-2

November 11, 2025Calculus of Variations and Partial Differential EquationsOpen Access

Variational properties of local functionals driven by arbitrary anisotropies

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Key Points

Relaxation results highlight variational properties in anisotropic local functionals, expanding on new integral representations.
Key findings indicate that bracket-generating assumptions are not necessary, enhancing flexibility in model application.
Analysis employs Lipschitz continuous vector fields to explore characteristics of local functionals without linear independence restrictions.
Variational properties in these settings support the potential for broader applications in mathematical and physical modeling.

Implication

This analysis reveals variational properties and relaxation results for anisotropic local functionals driven by continuous vector fields.

Abstract

We provide integral representation, Γ Γ -compactness and relaxation results for anisotropic local functionals depending on arbitrary Lipschitz continuous vector fields. In particular, neither bracket-generating assumptions nor linear independence conditions are required.

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Cite This Study

Verzellesi et al. (2025) studied this question.

synapsesocial.com/papers/69252e9ec0ce034ddc35651e https://doi.org/10.1007/s00526-025-03176-2

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Variational properties of local functionals driven by arbitrary anisotropies

Key Points

Implication

Abstract

Discussion

Cite This Study

Variational properties of local functionals driven by arbitrary anisotropies

Key Points

Implication

Abstract

Discussion

Cite This Study

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