Simultaneous recovery of piecewise analytic coefficients in a semilinear elliptic equation

Abstract

In this short note, we investigate simultaneous recovery inverse problems for semilinear elliptic equations with partial data. The main technique is based on higher order linearization and monotonicity approaches. With these methods at hand, we can determine the diffusion, cavity and coefficients simultaneously by knowing the corresponding localized Dirichlet-Neumann operators.

References in corpus (5)

• Simultaneous recoveries for semilinear parabolic systems
• Shape Reconstruction in Linear Elasticity: Standard and Linearized Monotonicity Method
• Monotonicity-Based Regularization for Shape Reconstruction in Linear Elasticity
• Determining a nonlinear hyperbolic system with unknown sources and nonlinearity
• Partial data inverse problems for quasilinear conductivity equations

Cited by in corpus (5)

• An inverse problem for a semilinear elliptic equation on conformally transversally anisotropic manifolds
• A radiation and propagation problem for a Helmholtz equation with a compactly supported nonlinearity
• Piecewise nonlinear materials and Monotonicity Principle
• Lipschitz stability estimate for the simultaneous recovery of two coefficients in the anisotropic Schrödinger type equation via local Cauchy data
• An inverse problem for semilinear equations involving the fractional Laplacian