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MR2817413 (2012e:35064) 35J60 (26B25 35B65 35J25 35J70 35J96 49L25)
Oberman, Adam M.; Silvestre, Luis The Dirichlet problem for the convex envelope. Trans. Amer. Math. Soc. 363 (2011), no. 11, 5871–5886.
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