Page 1

Displaying 1 – 2 of 2

Showing per page

Hilbert transforms and the Cauchy integral in euclidean space

Andreas Axelsson, Kit Ian Kou, Tao Qian (2009)

Studia Mathematica

We generalize the notions of harmonic conjugate functions and Hilbert transforms to higher-dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These harmonic conjugates are in general far from being unique, but under suitable boundary conditions we prove existence and uniqueness of conjugates. The proof also yields invertibility results for a new class of generalized double layer potential operators on Lipschitz surfaces and boundedness of related Hilbert...

Hypersingular integral equations and applications to porous elastic materials with periodic cracks

Michele Ciarletta, Gerardo Iovane (2005)

Bollettino dell'Unione Matematica Italiana

In this work a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions, is presented. The first goal of the present study is the development of an efficient analytical and direct numerical collocation method. The second one is the application of the method to the porous elastic materials when a periodic array of co-planar cracks is present. Starting from Cowin- Nunziato model...

Currently displaying 1 – 2 of 2

Page 1