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January/February 2012 On the Laplacian and fractional Laplacian in an exterior domain
Leonardo Kosloff, Tomas Schonbek
Adv. Differential Equations 17(1/2): 173-200 (January/February 2012).

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.

Citation

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Leonardo Kosloff. Tomas Schonbek. "On the Laplacian and fractional Laplacian in an exterior domain." Adv. Differential Equations 17 (1/2) 173 - 200, January/February 2012.

Information

Published: January/February 2012
First available in Project Euclid: 17 December 2012

zbMATH: 1248.35132
MathSciNet: MR2906733

Subjects:
Primary: 35J05, 35P05, 35Q30, 35Q35

Rights: Copyright © 2012 Khayyam Publishing, Inc.

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Vol.17 • No. 1/2 • January/February 2012
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