Transference of fractional Laplacian regularity
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1
Universidad de La Rioja
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2
University of Texas at Austin
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ISBN: 9783319105444
Ano de publicación: 2014
Volume: 108
Páxinas: 203-212
Tipo: Capítulo de libro
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Resumo
In this note we show how to obtain regularity estimates for the fractional Laplacian on the multidimensional torus Tn from the fractional Laplacian on ℝn. Though at first glance this may seem quite natural, it must be carefully precised. A reason for that is the simple fact that L2functions on the torus cannot be identified with L2functions on ℝn. The transference is achieved through a formula that holds in the distributional sense. Such an identity allows us to transfer Harnack inequalities, to relate the extension problems, and to obtain pointwise formulas and Hölder regularity estimates. © Springer International Publishing Switzerland 2014.