Abstract:The local boundedness of weak solutions to variational inequalities (obstacle problem) with the linear growth condition is obtained. Consequently, an analogue of a theorem by Reshetnyak about a.e. differentiability of weak solutions to elliptic divergence type differential equations is proved for variational inequalities.
Keywords: quasi-linear elliptic equations and inequalities, weak solution, local boundedness, pointwise differentiability, difference quotient
AMS Subject Classification: 35B65, 35J60, 35R45