论文标题
关于完全非线性椭圆pde的$ l^\ infty $中的反源识别问题
On the inverse source identification problem in $L^\infty$ for fully nonlinear elliptic PDE
论文作者
论文摘要
在本文中，我们概括了[N。 katzourakis，一种针对椭圆方程的反源识别问题的$ l^\ infty $正则化策略，Siam J. Math。肛门。 51：2，1349-1370（2019）]通过研究识别完全非线性椭圆方程的来源的错误问题。我们假设通过完全非线性观察操作员设置的紧凑型解决方案的差异数据和一些部分噪声信息。我们通过引入两参数Tykhonov正规化，以$ l^2 $“粘度术语”引入$ l^\ infty $最小化问题，从而处理了问题的高度非线性非概念性质以及缺乏弱连续性，并且可以通过微弱的半连续成本函数来近似。
In this paper we generalise the results proved in [N. Katzourakis, An $L^\infty$ regularisation strategy to the inverse source identification problem for elliptic equations, SIAM J. Math. Anal. 51:2, 1349-1370 (2019)] by studying the ill-posed problem of identifying the source of a fully nonlinear elliptic equation. We assume Dirichlet data and some partial noisy information for the solution on a compact set through a fully nonlinear observation operator. We deal with the highly nonlinear nonconvex nature of the problem and the lack of weak continuity by introducing a two-parameter Tykhonov regularisation with a higher order $L^2$ "viscosity term" for the $L^\infty$ minimisation problem which allows to approximate by weakly lower semicontinuous cost functionals.
