Revista Matemática Iberoamericana

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Volume 28, Issue 2, 2012, pp. 577–590
DOI: 10.4171/rmi/685

Published online: 2012-04-22

On the time derivative in an obstacle problem

Peter Lindqvist[1]

(1) Norwegian University of Science and Technology, Trondheim, Norway

We prove that the time derivative of the solution for the obstacle problem related to the evolutionary $p$-Laplace equation exists in Sobolev’s sense, provided that the given obstacle is smooth enough. We keep $p \geq 2$.

Keywords: Obstacle problem, time derivative, parabolic variational inequality

Lindqvist Peter: On the time derivative in an obstacle problem. Rev. Mat. Iberoam. 28 (2012), 577-590. doi: 10.4171/rmi/685