Extremal Solutions for Semilinear Obstacle Problems

Abstract

In this paper we establish the existence of a minimum solution bounded above by an upper solution for a parabolic problem with unilateral constraint (obstacle problem). Our approach uses truncation and penalization techniques and ultimately relies on Zorn's lemma.

Keywords:

• variational inequality,
• obstacl,
• subdifferential,
• strong solution,
• evolution equation,
• upper solution,
• Zorn's lemma