Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities

2019/09/17 by Katya Krupchyk, Gunther Uhlmann, Krupchyk, Katya +1 · 1 citation
Mathematics · #35J61 #35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35J61 #msc:35R30

paper · pdf · doi:10.48550/arxiv.1909.08122

arxiv created 2019/09/17 · arxiv updated 2019/09/19

Abstract

We show that the linear span of the set of scalar products of gradients of harmonic functions on a bounded smooth domain Ω⊂ ℝⁿ which vanish on a closed proper subset of the boundary is dense in L¹(Ω). We apply this density result to solve some partial data inverse boundary problems for a class of semilinear elliptic PDE with quadratic gradient terms.

Cited by

• X-ray imaging from nonlinear waves: numerical reconstruction of a cubic nonlinearity

Related

• Partial data inverse problems for quasilinear conductivity equations
• A remark on partial data inverse problems for semilinear elliptic equations
• Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations
• Inverse problems for semilinear elliptic equations with low regularity
• On the linearized local Calderon problem