In this paper, we consider the identical zero obstacle problem for the second order elliptic equation
where is an open bounded domain of . We prove that the free boundary has finite -Hausdorff measure, which extends the previous works by Caffarelli, Lee and Shahgholian for -Laplacian equations with respectively and contains the singular case of .
Cite this article
Jun Zheng, Peihao Zhao, A Remark on Hausdorff Measure in Obstacle Problems. Z. Anal. Anwend. 31 (2012), no. 4, pp. 427–439DOI 10.4171/ZAA/1467