# New trends in free boundary problems

## TL;DR

This paper reviews recent advances in free boundary problems that incorporate nonlocal interactions or nonlinear energy components, challenging classical assumptions and expanding the scope of the field.

## Contribution

It introduces new classes of free boundary problems with nonlocal and nonlinear features, providing novel theoretical insights beyond classical models.

## Key findings

- Identification of nonlocal effects in free boundary problems
- Analysis of nonlinear superpositions of energy components
- Extension of classical theory to more complex problem classes

## Abstract

We present a series of recent results on some new classes of free boundary problems. Differently from the classical literature, the problems considered have either a "nonlocal" feature (e.g., the interaction or/and the interfacial energy may depend on global quantities) or a "nonlinear" flavor (namely, the total energy is the nonlinear superposition of energy components, thus losing the standard additivity and scale invariances of the problem).