# Increasing stability for the inverse problem for the Schr\"odinger equation

## TL;DR

This paper investigates how the stability of determining a potential in the Schrödinger equation improves with more data, even when the potential has Sobolev regularity and is not compactly supported.

## Contribution

It extends previous results by handling Sobolev regular potentials and non-compact support, under flat boundary conditions and partial data.

## Key findings

- Demonstrates increasing stability with partial boundary data
- Handles Sobolev regular potentials
- Allows potentials that are not compactly supported

## Abstract

In this article, we study the increasing stability property for the determination of the potential in the Schr\"odinger equation from partial data. We shall assume that the inaccessible part of the boundary is flat and homogeneous boundary condition is prescribed on this part. In contrast to earlier works, we are able to deal with the case when potentials have some Sobolev regularity and also need not be compactly supported inside the domain.