# Regularity results and parametrices of semi-linear boundary problems of product type

## TL;DR

This paper presents a construction of parametrices for semi-linear elliptic boundary problems of product type, combining Boutet de Monvel calculus and paradifferential operators to handle linear and non-linear parts.

## Contribution

It introduces a novel method for constructing parametrices for semi-linear boundary problems using a hybrid approach of pseudo-differential and paradifferential calculus.

## Key findings

- Effective parametrix construction for semi-linear elliptic boundary problems.
- Enhanced understanding of boundary regularity in non-linear PDEs.
- Framework applicable to a broad class of non-linear boundary value problems.

## Abstract

This short note describes the benefit one obtains from a specific construction of a family of parametrices for a class of elliptic boundary value problems perturbed by non-linear terms of product type. The construction is based on the Boutet de Monvel calculus of pseudo-differential boundary operators for the linear elliptic parts, and on paradifferential operators for the product terms.