Abstract
Starting from the discussion of the Cauchy problem for a vibrating infinite string as a motivational example, the notion of a weak derivative is introduced as a mean of extending the notion of solution to a more general setting, where the functions involved may lack standard pointwise differentiability properties. Here two classes of test functions are also defined and discussed.
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Mitrea, D. (2018). Weak Derivatives. In: Distributions, Partial Differential Equations, and Harmonic Analysis. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-030-03296-8_1
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DOI: https://doi.org/10.1007/978-3-030-03296-8_1
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-03295-1
Online ISBN: 978-3-030-03296-8
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