论文标题
基于单调性的分数半线性椭圆方程的反转，具有功率类型非线性
Monotonicity-based inversion of fractional semilinear elliptic equations with power type nonlinearities
论文作者
论文摘要
我们研究了具有功率类型非线性的分数半线性椭圆方程的单调性方法。我们证明，如果系数与迪利奇（Dirichlet）到neumann地图的衍生物之间的单调关系，则仅由单调性关系。基于强大的单调关系，我们研究了针对分数calderón类型反问题的系数和包含检测的建设性全球唯一性。同时，我们还可以通过有限的测量来得出Lipschitz稳定性。任何$ n \ geq 1 $ $。
We investigate the monotonicity method for fractional semilinear elliptic equations with power type nonlinearities. We prove that if-and-only-if monotonicity relations between coefficients and the derivative of the Dirichlet-to-Neumann map hold. Based on the strong monotonicity relations, we study a constructive global uniqueness for coefficients and inclusion detection for the fractional Calderón type inverse problem. Meanwhile, we can also derive the Lipschitz stability with finitely many measurements. The results hold for any $n\geq 1$.
