Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities
Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities
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DOI：
10.4310/mrl.2020.v27.n6.a10
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发表时间：
2019-09
影响因子：
1
通讯作者：
Katya Krupchyk;G. Uhlmann
中科院分区：
文献类型：
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作者：
Katya Krupchyk;G. Uhlmann
证明了在边界的闭真子集上消失的有界光滑区域$\Omega\子集\Mathbb{R}^n上的调和函数梯度的标量积集合的线性跨度在$L^1(\Omega)$中稠密.我们将这一密度结果应用于求解一类带二次梯度项的半线性椭圆型偏微分方程解的部分数据逆边界问题。
We show that the linear span of the set of scalar products of gradients of harmonic functions on a bounded smooth domain $\Omega\subset \mathbb{R}^n$ which vanish on a closed proper subset of the boundary is dense in $L^1(\Omega)$. We apply this density result to solve some partial data inverse boundary problems for a class of semilinear elliptic PDE with quadratic gradient terms.