论文标题
确定具有功率类型非线性的椭圆方程的无界潜力
Determining an unbounded potential for an elliptic equation with a power type nonlinearity
论文作者
论文摘要
在本文中，我们关注半线性椭圆方程的反问题。我们表明，可以从完整的和部分的dirichlet到neumann地图确定潜在的$ q $ in $ l^{n/2+\ varepsilon} $，$ \ varepsilon> 0 $。这扩展了[M. Lassas，T。Liimatainen，Y.-H。 Lin和M. Salo，部分数据逆问题以及半线性椭圆方程的边界和系数的同时恢复，Rev. Mat。 iberoam。 （2021）]在Hölder连续电势方面显示了这一点。另外，我们还表明，当dirichlet到neumann地图仅限于边界上的一个点时，可以确定$ l^{n+\ varepsilon} $中的潜在$ q $。 Arxiv的作者：2202.05290 [Math.ap]证明这对于Hölder持续潜力是正确的。
In this article we focus on inverse problems for a semilinear elliptic equation. We show that a potential $q$ in $L^{n/2+\varepsilon}$, $\varepsilon>0$, can be determined from the full and partial Dirichlet-to-Neumann map. This extends the results from [M. Lassas, T. Liimatainen, Y.-H. Lin, and M. Salo, Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations, Rev. Mat. Iberoam. (2021)] where this is shown for Hölder continuous potentials. Also we show that when the Dirichlet-to-Neumann map is restricted to one point on the boundary, it is possible to determine a potential $q$ in $L^{n+\varepsilon}$. The authors of arXiv:2202.05290 [math.AP] proved this to be true for Hölder continuous potentials.
