Stable determination of the nonlinear term in a quasilinear elliptic equation by boundary measurements

TL;DR

This paper proves a Lipschitz stability inequality for identifying nonlinear terms in quasilinear elliptic equations using boundary measurements, employing linearization and special solutions.

Contribution

It introduces a novel stability estimate for the inverse problem of recovering nonlinear terms from boundary data in elliptic equations.

Findings

Established Lipschitz stability inequality for nonlinear term identification.

Used linearization and fundamental solutions for the proof.

Provides a method for stable recovery of nonlinearities.

Abstract

We establish a Lipschitz stability inequality for the problem of determining the nonlinear term in a quasilinear elliptic equation by boundary measurements. We give a proof based on a linearization procedure together with special solutions constructed from the fundamental solution of the linearized problem.