Differentiability in perturbation parameter of measure solutions to perturbed transport equation Article Swipe

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Differentiable function Bounded function Banach space Perturbation (astronomy) Mathematics Radon measure Mathematical analysis Singular perturbation Parameter space Perturbation theory (quantum mechanics) Physics Pure mathematics Quantum mechanics Locally compact space Statistics

Piotr Gwiazda , Sander C. Hille , Kamila Łyczek , Agnieszka Świerczewska-Gwiazda ·

YOU? · · 2019 · Open Access · · DOI: https://doi.org/10.3934/krm.2019041 · OA: W2963249632

We consider a linear perturbation in the velocity field of the transport equation. We investigate solutions in the space of bounded Radon measures and show that they are differentiable with respect to the perturbation parameter in a proper Banach space, which is predual to the Hölder space $ \mathcal{C}^{1+\alpha}( {\mathbb{R}^d}) $. This result on differentiability is necessary for application in optimal control theory, which we also discuss.