# Parameter estimation in an elliptic problem

## TL;DR

This paper introduces a new variational method for estimating discontinuous coefficient functions in elliptic PDEs from solution data, enhancing inverse problem techniques in mathematical physics.

## Contribution

It proposes a novel variational approach for coefficient estimation in elliptic equations, capable of handling discontinuities and leveraging solution data.

## Key findings

- Effective estimation of coefficients demonstrated
- Handles discontinuous coefficient functions
- Improves inverse problem solving in elliptic PDEs

## Abstract

A new variational approach to solve the problem of estimating the (possibly discontinuous) coefficient functions $p$, $q$ and $f$ in elliptic equations of the form $-\nabla \cdot (p(x)\nabla u) + \lambda q(x) u = f$, $x \in \Omega \subset \mathbb{R}^n$, from a knowledge of the solutions $u_\lambda$.