Solution of Laplace’s equation in a singular domain using Mellin transform. (English) Zbl 1507.44001
Summary: This paper deals with the theory of V. Kondratiev which allows to study the regularity of elliptical problems in corner domains. After having introduced the Mellin transform and the Sobolev spaces to weight, we recall the links with Sobolev spaces. The Mellin transform represent an important key to study the \(H^s\) regularity in corner domains.
MSC:
| 44A15 | Special integral transforms (Legendre, Hilbert, etc.) |
| 44A45 | Classical operational calculus |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 60H40 | White noise theory |
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