Uniform estimates for the Penalized Boundary Obstacle Problem
Rohit Jain · arXiv (Cornell University) · 2015
In this paper, motivated by a problem arising in random homogenization theory, we initiate the study of uniform estimates for the fractional penalized obstacle problem, $ Δ^{s}u^ε = β_ε (u^ε)$. In particular we consider the penalized boundary obstacle problem, $s = \frac{1}{2}$, and obtain sharp estimates for the solution independent of the penalizing parameter $ε$. This is a generalization of a result due to H. Brezis and D. Kinderlehrer.