New monotonicity formulas and the optimal regularity in the Signorini problem with variable coefficients
New monotonicity formulas and the optimal regularity in the Signorini problem with variable coefficients
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变系数Signorini问题中新的单调性公式和最优正则性
DOI：
10.1016/j.aim.2014.05.021
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发表时间：
2014
影响因子：
1.7
通讯作者：
Mariana Smit Vega Garcia
中科院分区：
文献类型：
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作者：
N. Garofalo;Mariana Smit Vega Garcia
我们研究具有 Lipschitz 连续系数的均匀椭圆发散形式算子 L= div (A (x)∇) 的内部 Signorini 或低维障碍问题。我们的主要结果表明，与 L= Δ 时发生的情况类似，当 M 是支撑障碍物的余维单平坦流形时，变分解具有最佳内部正则性 C loc 1, 1 2 (Ω±∪ M)。我们通过证明一些新的单调性公式来适当推广著名的阿尔姆格伦频率泛函来实现这一目标。
We study the interior Signorini, or lower-dimensional obstacle problem for a uniformly elliptic divergence form operator L= div (A (x)∇) with Lipschitz continuous coefficients. Our main result states that, similarly to what happens when L= Δ, the variational solution has the optimal interior regularity C loc 1, 1 2 (Ω±∪ M), when M is a codimension one flat manifold which supports the obstacle. We achieve this by proving some new monotonicity formulas for an appropriate generalization of the celebrated Almgren's frequency functional.