Advances in Differential Equations

The Stokes resolvent in 3D domains with conical boundary points: nonregularity in $L^p$-spaces

Paul Deuring

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Abstract

It is shown that solutions of the 3D Stokes resolvent problem in domains with conical boundary points, under homogeneous Dirichlet boundary conditions, do not satisfy the usual resolvent estimate in $L^p$-spaces if $p $ is close to infinity or close to $1.$

Article information

Source
Adv. Differential Equations Volume 6, Number 2 (2001), 175-228.

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1357141493

Mathematical Reviews number (MathSciNet)
MR1799750

Zentralblatt MATH identifier
1038.35053

Subjects
Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10]
Secondary: 35J55 76D07: Stokes and related (Oseen, etc.) flows

Citation

Deuring, Paul. The Stokes resolvent in 3D domains with conical boundary points: nonregularity in $L^p$-spaces. Adv. Differential Equations 6 (2001), no. 2, 175--228. https://projecteuclid.org/euclid.ade/1357141493.


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