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

• DOI: 10.1515/anona-2023-0110
• Publication Date: 2024-01-16T16:52:45Z
• 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)

Abstract We prove improved differentiability results for relaxed minimisers of vectorial convex functionals with

(

p , q

)

\left(p,q)

-growth, satisfying a Hölder-growth condition in

x

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.