Advances in Differential Equations

On the Laplacian and fractional Laplacian in an exterior domain

Leonardo Kosloff and Tomas Schonbek

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Abstract

We see that the generalized Fourier transform due to A.G. Ramm for the case of $n=3$ space dimensions remains valid, with some modifications, for all space dimensions $n\ge 2$. We use the resulting spectral representation of the exterior Laplacian to study exterior problems. In particular the Fourier splitting method developed by M.E. Schonbek extends easily to the study of this type of problems, as we illustrate for the dissipative 2-dimensional quasi-geostrophic equation in the critical case.

Article information

Source
Adv. Differential Equations Volume 17, Number 1/2 (2012), 173-200.

Dates
First available in Project Euclid: 17 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355703101

Mathematical Reviews number (MathSciNet)
MR2906733

Zentralblatt MATH identifier
1248.35132

Subjects
Primary: 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx] 35P05: General topics in linear spectral theory 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 35Q35: PDEs in connection with fluid mechanics

Citation

Kosloff, Leonardo; Schonbek, Tomas. On the Laplacian and fractional Laplacian in an exterior domain. Adv. Differential Equations 17 (2012), no. 1/2, 173--200. https://projecteuclid.org/euclid.ade/1355703101.


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