We give a form-perturbation theory by singular potentials for scalar elliptic operators on L2(Rd) of order 2m with Hölder continuous coefficients. The form-bounds are obtained from an L1 functional analytic approach which takes advantage of both the existence of m-gaussian kernel estimates and the holomorphy of the semigroup in L1(Rd). We also explore the (local) Kato class potentials in terms of (local) weak compactness properties. Finally, we extend the results to elliptic systems and singular matrix potentials. This article is part of the theme issue ‘Semigroup applications everywhere’.

中文翻译：

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高阶椭圆算子和奇异势系的形式摄动理论

我们给出了具有 Hölder 连续系数的 2m 阶 L2(Rd) 上的标量椭圆算子的奇异势形扰动理论。形式界是从 L1 泛函分析方法获得的，该方法利用了 m-高斯核估计的存在和 L1(Rd) 中半群的全纯性。我们还根据（局部）弱紧致性特性探索（局部）Kato 类势。最后，我们将结果扩展到椭圆系统和奇异矩阵势。这篇文章是主题问题“无处不在的半组应用程序”的一部分。