On exact solutions of Hankel equations

Petrov, V. E.

doi:10.1090/spmj/1534

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2020

2022

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Cited by 3 publications

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“…Therefore, investigating regularity of the solution, we use a special integral transformation P on the interval, which was introduced and studied in [P1]. Earlier, application of the transform P made it possible to solve many problems on the interval, which were previously either solved in a much more laborious way [P2], or remained open [AP,P3]. The definition and the main properties of P are described in Section 2.…”

Section: Resultsmentioning

confidence: 99%

Regularity of the solution of the Prandtl equation

Petrov¹,

Suslina²

2020

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Solvability and regularity of the solution of the Dirichlet problem for the Prandtl equationWe introduce the scale of spaces H s (−1, 1) in terms of the special integral transformation on the interval (−1, 1). We obtain theorem about existence and uniqueness of the solution in the classes H s (−1, 1) with 0 s 1. In particular, for s = 1 the result is as follows: if r 1/2 f ∈ L2, then r −1/2 u, r 1/2 u ′ ∈ L2, where r(x) = 1 − x 2 .

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Section: Resultsmentioning

confidence: 99%