Maximum principle and existence of Lp-viscosity solutions for fully nonlinear uniformly elliptic equations with measurable and quadratic terms

被引：22

作者：

Koike, S ^{[1
]}

Swiech, A

机构：

[1] Saitama Univ, Dept Math, Urawa, Saitama 3388570, Japan

[2] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2004年 / 11卷 / 04期

关键词：

L-p-viscosity solution; fully nonlinear equation; uniformly elliptic equation; maximum principle;

D O I：

10.1007/s00030-004-2001-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study L-p-viscosity solutions of fully nonlinear, second-order, uniformly elliptic partial differential equations (PDE) with measurable terms and quadratic nonlinearity. We present a sufficient condition under which the maximum principle holds for L-p-viscosity solution. We also prove stability and existence results for the equations under consideration.

引用

页码：491 / 509

页数：19

共 16 条

[1] Maximum principle and existence of Lp-viscosity solutions for fully nonlinear uniformly elliptic equations with measurable and quadratic terms
Shigeaki Koike
Andrzej Świch
Nonlinear Differential Equations and Applications NoDEA, 2004, 11 : 491 - 509
[2] On the ABP maximum principle for Lp-viscosity solutions of fully nonlinear PDE
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[3] POINTWISE PROPERTIES OF Lp-VISCOSITY SOLUTIONS OF UNIFORMLY ELLIPTIC EQUATIONS WITH QUADRATICALLY GROWING GRADIENT TERMS
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[9] REMARKS ON THE PHRAGMEN-LINDELOF THEOREM FOR Lp-VISCOSITY SOLUTIONS OF FULLY NONLINEAR PDES WITH UNBOUNDED INGREDIENTS
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[10] Existence of Solutions to Fully Nonlinear Elliptic Equations with Gradient Nonlinearity
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