Interior gradient estimates for solutions to the linearized Monge-Ampère equation
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Journal ArticleDate
2011-11-10Author
Gutiérrez, CENguyen, T
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http://hdl.handle.net/20.500.12613/6021
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10.1016/j.aim.2011.06.035Abstract
Let φ be a convex function on a convex domain Sigma;CRn, n≥1. The corresponding linearized Monge-Ampère equation is. trace(φD2u)=f, where φ:=detD2φ(D2φ)-1 is the matrix of cofactors of D2φ. We establish interior Hölder estimates for derivatives of solutions to such equation when the function f on the right-hand side belongs to Lp(Ω) for some p>n. The function φ is assumed to be such that φbSigma;C(Ω) with φ=0 on ∂. Ω and the Monge-Ampère measure detD2φ is given by a density gSigma;C(Sigma;) which is bounded away from zero and infinity. © 2011 Elsevier Inc.Citation to related work
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http://dx.doi.org/10.34944/dspace/6003