# A remark on partial data inverse problems for semilinear elliptic equations

## TL;DR

This paper proves that partial boundary measurements uniquely determine the nonlinearity in certain semilinear elliptic equations, advancing inverse problem theory.

## Contribution

It establishes the uniqueness of the nonlinearity in semilinear elliptic equations from partial boundary data, a significant extension of inverse problem results.

## Key findings

- Partial Dirichlet-to-Neumann map determines nonlinearity uniquely
- Results hold for arbitrary open boundary portions
- Advances inverse problems for semilinear elliptic equations

## Abstract

We show that the knowledge of the Dirichlet-to-Neumann map on an arbitrary open portion of the boundary of a domain in $\mathbb{R}^n$, $n\ge 2$, for a class of semilinear elliptic equations, determines the nonlinearity uniquely.