论文标题
几乎最小化的具有自由边界的均方根系统
Almost minimizers for a sublinear system with free boundary
论文作者
论文摘要
我们研究了能量功能的几乎最小化的矢量值$$ \ int_d \ left（| \ nabla \ mathbf {u} |^2+\ frac2 {1+q} \ left（λ_+（x）| \ mathbf { u}^+|^{q+1}+λ_-（x）| \ mathbf {u}^ - |^ - |^{q+1} \ right）\ right）dx，\ quad0 <q <q <1。$$对于Hölder连续系数$λ_\ pm（x）> 0 $，我们采用Epiperimetric不平等方法，并证明几乎最小化器和一组“常规”自由边界点的规律性。
We study vector-valued almost minimizers of the energy functional $$\int_D\left(|\nabla\mathbf{u}|^2+\frac2{1+q}\left(λ_+(x)|\mathbf{u}^+|^{q+1}+λ_-(x)|\mathbf{u}^-|^{q+1}\right)\right)dx,\quad0<q<1.$$ For Hölder continuous coefficients $λ_\pm(x)>0$, we take the epiperimetric inequality approach and prove the regularity for both almost minimizers and the set of "regular" free boundary points.
