Boundary regularity results for minimisers of convex functionals with (<i>p, q</i>)-growth
Boundary regularity results for minimisers of convex functionals with (<i>p, q</i>)-growth
Abstract We prove improved differentiability results for relaxed minimisers of vectorial convex functionals with <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>p</m:mi> <m:mo>,</m:mo> <m:mi>q</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> \left(p,q) -growth, satisfying a Hölder-growth condition in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>x</m:mi> </m:math> x . We consider both Dirichlet and Neumann boundary data. In addition, we …