论文标题
从裂缝的边缘进行独特的延续
Unique continuation from the edge of a crack
论文作者
论文摘要
在这项工作中，我们为具有裂缝的域中的一类椭圆方程开发了一个almgren型的单调性公式，而在有潜力的存在下，就相对于逆向重量的可忽略性条件或某些合适的集成性属性。基于构建一系列常规集，该序列的研究需要使用近似值，该研究的研究围绕裂纹边缘的一个点（裂缝边缘高度不平滑）的研究需要使用近似参数，该序列的序列是近似裂纹域的序列。一旦显示出Almgren频率的有限极限，对缩放溶液的爆炸分析使我们能够证明渐近膨胀和从裂纹边缘的强烈独特延续。
In this work we develop an Almgren type monotonicity formula for a class of elliptic equations in a domain with a crack, in the presence of potentials satisfying either a negligibility condition with respect to the inverse-square weight or some suitable integrability properties. The study of the Almgren frequency function around a point on the edge of the crack, where the domain is highly non-smooth, requires the use of an approximation argument, based on the construction of a sequence of regular sets which approximate the cracked domain. Once a finite limit of the Almgren frequency is shown to exist, a blow-up analysis for scaled solutions allows us to prove asymptotic expansions and strong unique continuation from the edge of the crack.
