Inverse problems in quasilinear anisotropic media

DOI10.1353/ajm.1997.0027zbMath0886.35176OpenAlexW2071134106MaRDI QIDQ4351041

Gunther Uhlmann, Ziqi Sun

Publication date: 10 May 1998

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://muse.jhu.edu/journals/american_journal_of_mathematics/toc/ajm119.4.html

zbMATH Keywords

uniquenessquasilinear boundary value problemanisotropic conductivitycurrent fluxvoltage potentialquasilinear anisotropic mediaquasilinear Dirichlet to Neumann map

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) PDEs in connection with optics and electromagnetic theory (35Q60) Inverse problems for PDEs (35R30)

Related Items (58)

Inverse problems for semilinear elliptic PDE with measurements at a single point ⋮ An Inverse Problem for the Porous Medium Equation with Partial Data and a Possibly Singular Absorption Term ⋮ An inverse problem for a fractional diffusion equation with fractional power type nonlinearities ⋮ An inverse problem for an inhomogeneous conformal Killing field equation ⋮ Simultaneous recoveries for semilinear parabolic systems ⋮ Inverse boundary value problems for a class of semilinear elliptic equations ⋮ AN INVERSE BOUNDARY VALUE PROBLEM FOR QUASILINEAR ELLIPTIC EQUATIONS ⋮ An inverse problem for a quasilinear convection-diffusion equation ⋮ Inverse problems for Lorentzian manifolds and non-linear hyperbolic equations ⋮ Inverse Transport and Diffusion Problems in Photoacoustic Imaging with Nonlinear Absorption ⋮ Uniqueness, reconstruction and stability for an inverse problem of a semi-linear wave equation ⋮ An inverse boundary value problem for certain anisotropic quasilinear elliptic equations ⋮ Cloaking for a quasi-linear elliptic partial differential equation ⋮ Inverse problems for elliptic equations with fractional power type nonlinearities ⋮ The Poisson embedding approach to the Calderón problem ⋮ On an inverse boundary value problem for a nonlinear time-harmonic Maxwell system ⋮ An inverse problem for a semi-linear elliptic equation in Riemannian geometries ⋮ Determining Lamé coefficients by the elastic Dirichlet-to-Neumann map on a Riemannian manifold ⋮ Remarks on the anisotropic Calderón problem ⋮ An inverse problem for a semilinear elliptic equation on conformally transversally anisotropic manifolds ⋮ Hölder stability for a semilinear elliptic inverse problem ⋮ A uniqueness theorem for inverse problems in quasilinear anisotropic media. II ⋮ Recovery of nonlinear terms for reaction diffusion equations from boundary measurements ⋮ Simultaneous recovery of piecewise analytic coefficients in a semilinear elliptic equation ⋮ Stable determination of the nonlinear term in a quasilinear elliptic equation by boundary measurements ⋮ An inverse problem for the Riemannian minimal surface equation ⋮ Increasing stability of a linearized inverse boundary value problem for a nonlinear Schrödinger equation on transversally anisotropic manifolds ⋮ Inverse problems for nonlinear magnetic Schrödinger equations on conformally transversally anisotropic manifolds ⋮ Determining a nonlinear hyperbolic system with unknown sources and nonlinearity ⋮ Partial data inverse problems for quasilinear conductivity equations ⋮ On the scientific work of Victor Isakov ⋮ A uniqueness theorem for inverse problems in quasilinear anisotropic media ⋮ The Calderón problem for quasilinear elliptic equations ⋮ Inverse problems for elliptic equations with power type nonlinearities ⋮ Inverse problems for nonlinear hyperbolic equations ⋮ Determination of viscosity in the stationary Navier-Stokes equations ⋮ The Calderón inverse problem for isotropic quasilinear conductivities ⋮ Recovery of coefficients for a weighted p-Laplacian perturbed by a linear second order term ⋮ Recovering a quasilinear conductivity from boundary measurements ⋮ Inverse Initial Boundary Value Problem for a Non-linear Hyperbolic Partial Differential Equation ⋮ On an inverse boundary value problem for a nonlinear elastic wave equation ⋮ Inverse problems: seeing the unseen ⋮ Reconstruction for the coefficients of a quasilinear elliptic partial differential equation ⋮ Inverse problem for the Yang-Mills equations ⋮ Recovering a variable exponent ⋮ Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations ⋮ Inverse problems for nonlinear Maxwell's equations with second harmonic generation ⋮ On an inverse problem for a fractional semilinear elliptic equation involving a magnetic potential ⋮ Direct and inverse problems for the nonlinear time-harmonic Maxwell equations in Kerr-type media ⋮ A remark on partial data inverse problems for semilinear elliptic equations ⋮ Stability estimate for a semilinear elliptic inverse problem ⋮ Reconstruction of the Collision Kernel in the Nonlinear Boltzmann Equation ⋮ Inverse problems for the fractional Laplace equation with lower order nonlinear perturbations ⋮ On the determination of nonlinear terms appearing in semilinear hyperbolic equations ⋮ A density property for tensor products of gradients of harmonic functions and applications ⋮ An inverse problem for the non-linear fractional magnetic Schrödinger equation ⋮ An inverse problem for the minimal surface equation ⋮ Lipschitz and Hölder stable determination of nonlinear terms for elliptic equations

This page was built for publication: Inverse problems in quasilinear anisotropic media