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Maximum principle and existence of \(L^p\)-viscosity solutions for fully nonlinear uniformly elliptic equations with measurable and quadratic terms. (English) Zbl 1079.49026

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.

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
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