Date of Award
2012
Document Type
Thesis
Publication Status
Version of Record
Submission Date
October 2026
Abstract
In this work, we develop an extension of the generalized Fourier transform for exterior domains due to T. Ikebe and A. Ramm for all dimensions n>2 to study the Laplacian, and fractional Laplacian operators in such a domain. Using the harmonic extension approach due to L. Caffarelli and L. Silvestre, we can obtain a localized version of the operator, so that it is precisely the square root of the Laplacian as a self-adjoint operator in L2 with DIrichlet boundary conditions. In turn, this allowed us to obtain a maximum principle for solutions of the dissipative two-dimensional quasi-geostrophic equation the exterior domain, which we apply to prove decay results using an adaptation of the Fourier Splitting method of M.E. Schonbek.
Extent
vi, 194 p. : ill.
Recommended Citation
Kosloff, Leonardo., "On the Laplacian and fractional Laplacian in exterior domains, and applications to the dissipative quasi-geostrophic equation" (2012). Electronic Theses and Dissertations 2010 - 2019. 597.
https://digitalcommons.fau.edu/etd_general_6/597
Identifier
FADT3355570
Comments
by Leonardo Kosloff.|Thesis (Ph.D.)--Florida Atlantic University, 2012.|Includes bibliography.|Mode of access: World Wide Web.|System requirements: Adobe Reader.|by Leonardo Kosloff.