# Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain

## TL;DR

This paper establishes a precise two-term asymptotic formula for the eigenvalues of the Dirichlet Laplacian in Lipschitz domains, providing new insights into spectral geometry and eigenvalue distribution.

## Contribution

It proves a two-term Weyl-type asymptotic formula for eigenvalues in Lipschitz domains and offers a universal bound for convex domains that captures the first two asymptotic terms.

## Key findings

- Derived a two-term asymptotic formula for eigenvalues
- Established a universal bound for convex domains
- Reproduces the first two terms of spectral asymptotics

## Abstract

We prove a two-term Weyl-type asymptotic formula for sums of eigenvalues of the Dirichlet Laplacian in a bounded open set with Lipschitz boundary. Moreover, in the case of a convex domain we obtain a universal bound which correctly reproduces the first two terms in the asymptotics.