论文标题
非平滑布鲁兹 - 奥斯瓦尔德的独特结果
A non-smooth Brezis-Oswald uniqueness result
论文作者
论文摘要
我们将非负关键点分类为$ w^{1，p} _0（ω）$ \ [j（v）= \int_Ω非侵害。由于$ h $可能没有可区分的，$ f $具有单方面的增长条件，因此$ j $仅是L.S.C.在$ w^{1，p} _0（ω）$上。我们对非平滑函数的关键点的弱概念较弱，在没有Euler-Lagrange方程的情况下得出后者的足够规律性，并通过非平滑的Picone不平等现象\ cite {bo}的唯一性部分。
We classify the non-negative critical points in $W^{1,p}_0(Ω)$ of \[ J(v)=\int_ΩH(Dv)-F(x, v)\, dx \] where $H$ is convex and positively $p$-homogeneous, while $t\mapsto \partial_tF(x, t)/t^{p-1}$ is non-increasing. Since $H$ may not be differentiable and $F$ has a one-sided growth condition, $J$ is only l.s.c. on $W^{1,p}_0(Ω)$. We employ a weak notion of critical point for non-smooth functionals, derive sufficient regularity of the latter without an Euler-Lagrange equation available and focus on the uniqueness part of the results in \cite{BO}, through a non-smooth Picone inequality.
