论文标题
Lipschitz的连续性结果
Lipschitz continuity results for a class of obstacle problems
论文作者
论文摘要
我们证明了Lipschitz的连续性结果，用于解决标准增长条件下的一类障碍问题的解决方案，$ p $ -type，$ p \ geq 2 $。主要的新颖性是使用线性化技术可以追溯到[28]，以解释我们受约束的最小化器作为对右侧有界的非线性椭圆方程的解决方案。这使我们启动了Moser迭代方案，该方案提供了为梯度绑定的$ l^\ infty $。最近的更高可区分性结果的应用[24]使我们能够简化[32]中使用的线性化技术中识别ra的过程的过程。据我们所知，这是具有标准生长条件在Lipschitz规律性方向的标准生长条件的非自治功能的第一个结果。
We prove Lipschitz continuity results for solutions to a class of obstacle problems under standard growth conditions of $p$-type, $p \geq 2$. The main novelty is the use of a linearization technique going back to [28] in order to interpret our constrained minimizer as a solution to a nonlinear elliptic equation, with a bounded right-hand side. This leads us to start a Moser iteration scheme which provides the $L^\infty$ bound for the gradient. The application of a recent higher differentiability result [24] allows us to simplify the procedure of the identification of the Radon measure in the linearization technique employed in [32]. To our knowledge, this is the first result for non-autonomous functionals with standard growth conditions in the direction of the Lipschitz regularity.
