An inverse boundary value problem for certain anisotropic quasilinear elliptic equations

Abstract

In this paper we prove uniqueness in the inverse boundary value problem for quasilinear elliptic equations whose linear part is the Laplacian and nonlinear part is the divergence of a function analytic in the gradient of the solution. The main novelty in terms of the result is that the coefficients of the nonlinearity are allowed to be "anisotropic". As in previous works, the proof reduces to an integral identity involving the tensor product of the gradients of 3 or more harmonic functions. Employing a construction method using Gaussian quasi-modes, we obtain a convenient family of harmonic functions to plug into the integral identity and establish our result.

References in corpus (2)

• Reconstruction for the coefficients of a quasilinear elliptic partial differential equation
• Recovery of coefficients for a weighted p-Laplacian perturbed by a linear second order term

Cited by in corpus (8)

• Simultaneous recoveries for semilinear parabolic systems
• An inverse problem for a semilinear elliptic equation on conformally transversally anisotropic manifolds
• An inverse problem for a quasilinear convection--diffusion equation
• A density property for tensor products of gradients of harmonic functions and applications
• The Calderón inverse problem for isotropic quasilinear conductivities
• On a nonlinear model in domains with cavities arising from cardiac electrophysiology
• An inverse boundary value problem for the inhomogeneous porous medium equation
• Two uniqueness results in the inverse boundary value problem for the weighted p-Laplace equation