# Removable sets in non-uniformly elliptic problems

## TL;DR

This paper investigates the properties of solutions to complex elliptic equations with variable structure, focusing on identifying which sets can be removed without affecting the solution's regularity, using advanced measure theory.

## Contribution

It provides a characterization of removable sets for Hölder continuous solutions in non-uniformly elliptic problems with double phase structure, advancing understanding of solution regularity.

## Key findings

- Characterization of removable sets via intrinsic Hausdorff measures
- Analysis of fine properties of solutions in double phase problems
- Extension of removable set theory to non-uniform elliptic equations

## Abstract

We analyze fine properties of solutions to quasilinear elliptic equations with double phase structure and characterize, in the terms of intrinsic Hausdorff measures, the removable sets for H\"older continuous solutions.