Interior gradient estimates for solutions to the linearized Monge-Ampère equation

• Autores: Cristian E. Gutiérrez, Truyen Nguyen
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 228, Nº 4, 2011, págs. 2034-2070
• Idioma: inglés
• DOI: 10.1016/j.aim.2011.06.035
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let phi be a convex function on a convex domain Omega subset of R-n, n >= 1. The corresponding linearized Monge-Ampere equation is trace(Phi D(2)u) = f, where Phi := det D-2 phi(D-2 phi)(-1) is the matrix of cofactors of D-2 phi. We establish interior Holder estimates for derivatives of solutions to such equation when the function f on the right-hand side belongs to L-p(Omega) for some p > n. The function phi is assumed to be such that phi is an element of C((Omega) over bar) with phi = 0 on partial derivative Omega and the Monge-Ampere measure det D-2 phi is given by a density g is an element of C(Omega) which is bounded away from zero and infinity. (C) 2011 Elsevier Inc. All rights reserved.

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