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 partially overdetermined boundary-value problem for Laplace PDE in a planar simply connected domain with Lipschitz boundary∂  ⁡  Ω${\partial\Omega}$   . Assuming Dirichlet and Neumann data available onΓ  ⊂   ∂  ⁡  Ω${\Gamma\subset\partial\Omega}$    to be real-valued functions inW    1  /  2   ,  2    ⁢   (  Γ  )${W^{1/2,2}(\Gamma)}$    andL  2   ⁢   (  Γ  )${L^{2}(\Gamma)}$    classes, respectively, we develop a non-iterative method for solving this ill-posed Cauchy problem choosingL  2${L^{2}}$    bound of the solution on∂  ⁡  Ω   ∖  Γ${\partial\Omega\setminus\Gamma}$    as a regularizing parameter. The present complex-analytic approach also naturally allows imposing additional pointwise constraints on the solution which, on practical side, can help incorporating outlying boundary measurements without changing the boundary into a less regular one.

Recovery of harmonic functions from partial boundary data respecting internal pointwise values