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

Shigeaki Koike; Andrzej Świȩch

doi:10.1007/s00030-004-2001-9

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

Shigeaki Koike, Andrzej Świȩch

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	491-509
Number of pages	19
Journal	Nonlinear Differential Equations and Applications
Volume	11
Issue number	4
DOIs	https://doi.org/10.1007/s00030-004-2001-9
Publication status	Published - 2004 Dec 1

Keywords

Fully nonlinear equation
L-viscosity solution
Maximum principle
Uniformly elliptic equation

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1007/s00030-004-2001-9

Cite this

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AU - Świȩch, Andrzej

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AB - We study Lp-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 Lp-viscosity solution. We also prove stability and existence results for the equations under consideration.

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KW - L-viscosity solution

KW - Maximum principle

KW - Uniformly elliptic equation

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