English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider a hypersurface in R  n   parametrized by a diffeomorphism  Φ  o  of the unit sphere in R  n   into R  n  , and we take a point  w  in the domain I[ Φ  o ] enclosed by the image of  Φ  o , and we consider the ‘hole’ R[ w  +  εξ ] enclosed by the image of the hypersurface  w  +  εξ , where  ξ  is a diffeomorism as  Φ  o  with 0 ∈ I[ ξ ] and  ε  is a small positive real parameter. Then we consider the Dirichlet problem for the Laplace equation in the perforated domain I[ Φ  o ] with the hole I[ w  +  εξ ] removed and show real analytic continuation properties of the solution  u  and of the corresponding energy integral as functionals of the sextuple of  w ,  ε ,  ξ ,  Φ  o   , and of the Dirichlet data in the interior and exterior boundaries of the perforated domain, which we think of as a point in an appropriate Banach space, around a degenerate sextuple with  ε  = 0.

Asymptotic behavior of the solutions of the Dirichlet problem for the Laplace operator in a domain with a small hole. A functional analytic approach