Boundary regularity results for minimisers of convex functionals with $(p,q)$-growth

Christopher Irving; Lukas Koch

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arXiv · 2212.14723

Boundary regularity results for minimisers of convex functionals with $(p,q)$-growth

Christopher Irving·Lukas Koch

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Abstract

We prove improved differentiability results for relaxed minimisers of vectorial convex functionals with $(p, q)$-growth, satisfying a H\"older-growth condition in $x$. We consider both Dirichlet and Neumann boundary data. In addition, we obtain a characterisation of regular boundary points for such minimisers. In particular, in case of homogeneous boundary conditions, this allows us to deduce partial boundary regularity of relaxed minimisers on smooth domains for radial integrands. We also obtain some partial boundary regularity results for non-homogeneous Neumann boundary conditions.

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Christopher Irving, Lukas Koch. 2022-12-30. Boundary regularity results for minimisers of convex functionals with $(p,q)$-growth. https://arxiv.org/abs/2212.14723

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