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

• DOI: 10.48550/arxiv.2212.14723
• Publication Date: 2022-01-01
• Authors: Christopher Irving; Lukas Koch
• Keywords: regular boundary points; QA299.6-433; 01 natural sciences; 35j70; 35j60; Mathematics - Analysis of PDEs; partial regularity; nonuniformly elliptic convex vectorial functionals; FOS: Mathematics; 0101 mathematics; non-autonomous integrands; Analysis; Analysis of PDEs (math.AP)

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