Estimates of Oseen kernels in weighted \(L^p\) spaces. (English) Zbl 0988.76021

Kračmar, Stanislav; Novotný, Antonín; Pokorný, Milan

J. Math. Soc. Japan 53, No. 1, 59-111 (2001).

The authors study convolutions with Oseen kernels (weakly singular and singular) in both two- and three-dimensional space. They develop a weighted \(L^p\) theory, \(p\in (1,\infty]\), for anisotropic weights.

Reviewer: Mirela Kohr (Cluj-Napoca)

MSC:

76D07	Stokes and related (Oseen, etc.) flows
42B20	Singular and oscillatory integrals (Calderón-Zygmund, etc.)
35C15	Integral representations of solutions to PDEs

Keywords:

Oseen fundamental solution; singular Oseen kernel; weighted \(L(p)\) space; anisotropic weight; weakly singular Oseen kernel