Advances in Differential Equations

On the Laplacian and fractional Laplacian in an exterior domain

Leonardo Kosloff and Tomas Schonbek

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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

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

First available in Project Euclid: 17 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

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