Boundary Properties and Applications of the Differentiated Poisson Integral for Different Domains
Sergo Topuria
This monograph is devoted to the investigation of boundary properties of the differentiated Poisson integral. It is proved that the boundary properties of the differentiated Poisson integral for different types of domains (circle, sphere, half-plane, half-space, bicylinder) differ substantially from each other and depend on in what sense the integral density is differentiable. The theorems proven here are, in a definite sense, improvable. Relying on the obtained results, the Dirichlet problem is solved for a sphere and a half-space (of any finite dimension) in the case where the boundary function is measurable and finite almost everywhere.
Catégories:
Année:
2009
Editeur::
Nova Science Pub Inc
Langue:
english
Pages:
191
ISBN 10:
1606927043
ISBN 13:
9781606927045
Collection:
Mathematics Research Developments
Fichier:
PDF, 1.28 MB
IPFS:
,
english, 2009