Koike, Shigeaki; Świȩch, Andrzej Maximum principle and existence of \(L^p\)-viscosity solutions for fully nonlinear uniformly elliptic equations with measurable and quadratic terms. (English) Zbl 1079.49026 NoDEA, Nonlinear Differ. Equ. Appl. 11, No. 4, 491-509 (2004). Summary: We study \(L^p\)-viscosity solutions of fully nonlinear, second-order, uniformly elliptic partial differential equations with measurable terms and quadratic nonlinearity. We present a sufficient condition under which the maximum principle holds for \(L^p\)-viscosity solutions. We also prove stability and existence results for the equations under consideration. Cited in 1 ReviewCited in 16 Documents MSC: 35J60 Nonlinear elliptic equations 35B50 Maximum principles in context of PDEs 35D10 Regularity of generalized solutions of PDE (MSC2000) 49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games 49J20 Existence theories for optimal control problems involving partial differential equations Keywords:\(L^p\)-viscosity solution; fully nonlinear equation; uniformly elliptic equation; maximum principle PDFBibTeX XMLCite \textit{S. Koike} and \textit{A. Świȩch}, NoDEA, Nonlinear Differ. Equ. Appl. 11, No. 4, 491--509 (2004; Zbl 1079.49026) Full Text: DOI