On global solutions of the obstacle problem

TL;DR

This paper proves a long-standing conjecture about the classification of global solutions to the obstacle problem with unbounded coincidence sets, under certain dimension assumptions.

Contribution

It provides a new classification result for global solutions of the obstacle problem, addressing a conjecture that has remained open for a long time.

Findings

Classification of global solutions with unbounded coincidence sets

Validation of the conjecture under dimension assumptions

Advancement in understanding obstacle problem solutions

Abstract

Assuming a lower bound on the dimension, we prove a long standing conjecture concerning the classification of global solutions of the obstacle problem with unbounded coincidence sets.