On a representation of fully nonlinear elliptic operators in terms of pure second order derivatives and its applications

被引：0

作者：

Krylov N.V. ^{[1
]}

机构：

[1] University of Minnesota, Minneapolis, MN 55455

来源：

Journal of Mathematical Sciences | 2011年 / 177卷 / 1期

基金：

美国国家科学基金会;

关键词：

Full Measure; Nonlinear Elliptic Equation; Relative Interior; Lipschitz Continuous Function; Convex Envelope;

D O I：

10.1007/s10958-011-0445-0

中图分类号：

学科分类号：

摘要：

We give a method of representing fully nonlinear elliptic operators given by boundedly inhomogeneous functions in terms of operators acting only on pure second order derivatives. We also discuss possible applications of such representations to using. Estimates for Second finite di. erence approximations for solving the corresponding equations. © 2011 Springer Science+Business Media, Inc.

引用

页码：1 / 26

页数：25

共 10 条

[1]

Krylov N.V., Bounded inhomogeneous nonlinear elliptic and parabolic equations in the plane, Math. USSR Sb., 11, 1, pp. 89-99, (1970)

[2]

Evans L.C., On solving certain nonlinear partial di.erential equations by accretive operator methods, Israel J. Math., 36, pp. 225-247, (1980)

[3]

Caffarelli L.S., Souganidis P.E., A rate of convergence for monotone finite difference approximations to fully nonlinear, uniformly elliptic PDEs, Comm. Pure Appl. Math., 61, 1, pp. 1-17, (2008)

[4]

Kuo H.-J., Trudinger N.S., Discrete methods for fully nonlinear elliptic equations, SIAM J. Numer. Anal., 29, 1, pp. 123-135, (1992)

[5]

Motzkin T., Wasow W., On the approximation of linear elliptic differential equations by difference equations with positive coefficients, J. Math. Phys., 37, pp. 253-259, (1953)

[6]

Krylov N.V., Interior Estimates for Second Di. erences for Finite-Di. erence Elliptic Bellman's Equations

[7]

Schmutz E., Rational points on the unit sphere, Cent. Eur. J. Math., 6, 3, pp. 482-487, (2008)

[8]

Krylov N.V., On factorizations of smooth nonnegative matrix-values functions and on smooth functions with values in polyhedra, Appl. Math. Optim., 58, 3, pp. 373-392, (2008)

[9]

Krylov N.V., Lectures on Elliptic and Parabolic Equations in Sobolev Spaces, (2008)

[10]

Evans L.C., Gariepy R.F., Measure Theory and Fine Properties of Functions, (1992)

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