论文标题
$（p，q）$ - 增长的凸功能最小值的边界规律性结果
Boundary regularity results for minimisers of convex functionals with $(p,q)$-growth
论文作者
论文摘要
我们证明，用$（P，Q）$ - 增长，可满足$ x $的Hölder-Growth条件的矢量凸功能的轻松最小化剂的可不同性结果。我们考虑Dirichlet和Neumann边界数据。此外，我们获得了此类最小化器的常规边界点的表征。特别是，在均匀的边界条件的情况下，这使我们能够推断出放松的极小剂在光滑域上的部分边界规则性，以用于径向积分。我们还为非均匀的诺伊曼边界条件获得了一些部分边界规律性结果。
We prove improved differentiability results for relaxed minimisers of vectorial convex functionals with $(p, q)$-growth, satisfying a Hölder-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.
