On boundary H\"older gradient estimates for solutions to the linearized Monge-Amp\`ere equations
Abstract
In this paper, we establish boundary H\"older gradient estimates for solutions to the linearized Monge-Amp\`ere equations with Lp (n<p≤∞) right hand side and C1,γ 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 C1, 1 boundary data.
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