# Extension of reilly formula for a class of elliptic differential operator in divergence form

## TL;DR

This paper extends the Reilly formula to a class of elliptic divergence operators involving Codazzi tensor fields and derives estimates for their first positive eigenvalues.

## Contribution

The paper introduces a generalized Reilly formula for elliptic divergence operators with Codazzi tensor fields, providing new eigenvalue estimates.

## Key findings

- Extended Reilly formula for a new class of elliptic operators
- Derived bounds for the first positive eigenvalue
- Applicable to operators with Codazzi tensor fields

## Abstract

We prove the Reilly formula for a class of elliptic divergence differential operator $L_Au=div(A\nabla u)$, where $A$ is a (1,1)-Codazzi tensor field. Then we get some estimates for the first positive eigenvalue of the operator.