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On boundary Hölder gradient estimates for solutions to the linearized Monge-Ampère equations (1303.3305v2)
Published 13 Mar 2013 in math.AP
Abstract: In this paper, we establish boundary H\"older gradient estimates for solutions to the linearized Monge-Amp`ere equations with $L{p}$ ($n<p\leq\infty$) right hand side and $C{1,\gamma}$ boundary values under natural assumptions on the domain, boundary data and the Monge-Amp`ere measure. These estimates extend our previous boundary regularity results for solutions to the linearized Monge-Amp`ere equations with bounded right hand side and $C{1, 1}$ boundary data.
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