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Thesis

Vectorial problems: sharp Lipschitz bounds and borderline regularity

Abstract:

This thesis is devoted to the proof of fine regularity properties of solutions to a broad class of variational problems including models from geometry, material science, continuum mechanics and particle physics. Our starting point is the analysis of the behavior of manifold-constrained minima to certain non-homogeneous functionals: under sharp assumptions, we prove that they are regular everywhere, except on a negligible, "singular" set of points. The presence of the singular set is in gen...

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Division:
MPLS
Department:
Mathematical Institute
Role:
Author

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Role:
Supervisor
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford

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