Chapter 2: The Spaces D ♭ $$\mathcal D^\flat $$, D ♯ $$\mathcal D^\sharp $$ and D ′ $$\mathcal D'$$: Elements of the Distribution Theory (Generalized Functions in the Sense of Schwartz)

A. S. Demidov
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A. S. Demidov: Lomonosov Moscow State University, Department of Mechanics and Mathematics

A chapter in Equations of Mathematical Physics, 2023, pp 71-90 from Springer

Abstract: Abstract The definition of the generalized solution u ∈ L l o c 1 $$u\in L_{loc}^1$$ to one or another problem of mathematical physics, as given by Sobolev (1936), and, in particular, Definition 11.6 is based on Theorem 10.1 and the Ostrogradsky–Gauss formula ( 7.3 ).

Date: 2023
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DOI: 10.1007/978-3-031-30358-6_2

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