• Citer

Positive powers of the laplacian: From hypersingular integrals to boundary value problems

par Abatangelo, Nicola ;Jarohs, Sven;Saldaña, Alberto
Référence Communications on pure and applied analysis, 17, 3, page (899-922)
Publication Publié, 2018-05

Article révisé par les pairs

• Détails
• Contenu

Résumé :

Any positive power of the Laplacian is related via its Fourier symbol to a hypersingular integral with finite differences. We show how this yields a pointwise evaluation which is more exible than other notions used so far in the literature for powers larger than 1; in particular, this evaluation can be applied to more general boundary value problems and we exhibit explicit examples. We also provide a natural variational framework and, using an asymptotic analysis, we prove how these hypersingular integrals reduce to polyharmonic operators in some cases. Our presentation aims to be as self-contained as possible and relies on elementary pointwise calculations and known identities for special functions.