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On the Lipschitz continuity of derivatives for some scalar nonlinearities. (English) Zbl 1152.47047

Author’s abstract: Vector nonlinearities determined by a scalar function arise in various mathematical models. The numerical solution of the corresponding partial differential equations often relies on the Lipschitz continuity of the derivative of the nonlinear operator. In this paper, a simple sufficient condition is given for the required Lipschitz continuity, also providing an easily computable estimate of the Lipschitz constant. Some discussion is included for the corresponding elliptic operators.

MSC:

47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
46T20 Continuous and differentiable maps in nonlinear functional analysis
46N20 Applications of functional analysis to differential and integral equations
35J60 Nonlinear elliptic equations
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