# Approximate convexity principles and applications to PDEs in convex domains

## TL;DR

This paper develops approximate convexity principles for solutions to certain nonlinear elliptic PDEs in convex domains, focusing on equations with nearly concave nonlinearities, and explores specific applications of these principles.

## Contribution

It introduces new approximate convexity principles for nonlinear elliptic PDEs with nearly concave nonlinearities in convex domains, expanding theoretical understanding.

## Key findings

- Established approximate convexity principles for specific PDE classes
- Demonstrated applications to meaningful special cases
- Enhanced understanding of solution behavior in convex domains

## Abstract

We obtain approximate convexity principles for solutions to some classes of nonlinear elliptic partial differential equations in convex domains involving approximately concave nonlinearities. Furthermore, we provide some applications to some meaningful special cases.