# Regularity properties of semilinear boundary problems in Besov and Triebel--Lizorkin spaces

## TL;DR

This paper investigates the regularity and existence of solutions to semi-linear elliptic boundary problems, including Navier--Stokes equations, within Besov and Triebel--Lizorkin spaces, addressing challenges posed by complex boundary conditions.

## Contribution

It provides new regularity and existence results for semi-linear elliptic boundary problems in advanced function spaces, handling high-class boundary conditions.

## Key findings

- Established regularity results in Besov and Triebel--Lizorkin spaces
- Addressed boundary condition difficulties for complex boundary classes
- Applied results to stationary Navier--Stokes equations

## Abstract

Semi-linear elliptic boundary problems with non-linearities of product type are considered, in particular the stationary Navier--Stokes equations. Regularity and existence results are dealt with in the Besov and Triebel--Lizorkin spaces, and it is explained how difficulties occurring for boundary conditions of a high class may be handled.