论文标题
Lipschitz和Hölder稳定确定椭圆方程的非线性术语
Lipschitz and Hölder stable determination of nonlinear terms for elliptic equations
论文作者
论文摘要
我们考虑确定边界测量中椭圆方程中出现的某些非线性术语的逆问题。更确切地说，我们研究了此类反问题的稳定性问题。在适当的假设下，我们证明了Lipschitz和Hölder稳定性估计值与确定在此类椭圆方程中出现的准线性和半线性项相关的测量，从限制在域边界的任意部分的测量值中。除了它们的数学兴趣外，我们的稳定性估计值可能有助于改善此类非线性术语的数值重建。我们的方法将线性化技术与适当类别溶液的应用相结合。
We consider the inverse problem of determining some class of nonlinear terms appearing in an elliptic equation from boundary measurements. More precisely, we study the stability issue for this class of inverse problems. Under suitable assumptions, we prove a Lipschitz and a Hölder stability estimate associated with the determination of quasilinear and semilinear terms appearing in this class of elliptic equations from measurements restricted to an arbitrary parts of the boundary of the domain. Besides their mathematical interest, our stability estimates can be useful for improving numerical reconstruction of this class of nonlinear terms. Our approach combines the linearization technique with applications of suitable class of singular solutions.
