W2,p-estimates for the linearized Monge-Ampere equation

被引：10

作者：

Gutierrez, Cristian E. ^{[1
]}

Tournier, Federico

机构：

[1] Temple Univ, Dept Math, Philadelphia, PA 19122 USA

[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2006年 / 358卷 / 11期

关键词：

a priori estimates of second derivatives; cross sections of solutions; viscosity solutions; nonuniformly elliptic equations;

D O I：

10.1090/S0002-9947-06-04189-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Omega subset of R-n be a strictly convex domain and let phi epsilon C-2 (Omega) be a convex function such that lambda <= detD(2)phi <= Lambda in Omega. The linearized Monge-Ampere equation is L(Phi)u = trace(Phi D(2)u) = f, where Phi = (detD(2)phi) (D-2 phi)(-1) is the matrix of cofactors of D-2 phi. We prove that there exist p > 0 and C > 0 depending only on n, lambda, Lambda, and dist(Omega', Omega) such that vertical bar vertical bar D(2)u vertical bar vertical bar(Lp)(Omega') <= C(vertical bar vertical bar u vertical bar vertical bar(L infinity(Omega)) + vertical bar vertical bar f vertical bar vertical bar(Ln(Omega))) for all solutions u is an element of C-2(Omega) to the equation L(Phi)u = f.

引用

页码：4843 / 4872

页数：30