On the mean oscillation of the Hessian of solutions to the Monge¿Ampère equation

• Autores: Qingbo Huang
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 207, Nº 2, 2006, págs. 599-616
• Idioma: inglés
• DOI: 10.1016/j.aim.2005.12.005
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• Resumen

  • We give interior a priori estimates for the mean oscillation of second derivatives of solutions to the Monge¿Ampère equation detD2u=f(x) with zero boundary values, where f(x) is a non-Dini continuous function. If the modulus of continuity of f(x) is f(r) such that limr?0f(r)log(1/r)=0, then D2uVMO.