Elliptic Obstacle Problems with Measurable Coefficients in Non-Smooth Domains

Abstract

We establish a global weighted W ^{1, p} -regularity for solutions to variational inequalities and obstacle problems for divergence form elliptic systems with measurable coefficients in bounded non-smooth domains.

Keywords:

• Elliptic obstacle problem
• Global weighted L ^p -estimates
• Measurable coefficients
• Reifenberg flat domain
• Small BMO

Mathematics Subject Classification:

• Primary 35J88
• Secondary 35R05

ACKNOWLEDGMENTS

S.-S. Byun was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (MEST) (2012-047030).

Part of the special issue, “Variational Analysis and Applications.”