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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Segregated direct boundary-domain integral equations (BDIEs) based on aparametrix and associated with the Dirichlet and Neumann boundary valueproblems for the linear stationary diffusion partial differential equation witha variable coefficient are formulated. The PDE right hand sides belong to theSobolev space $H^{-1}(\Omega)$ or $\tilde H^{-1}(\Omega)$, when neitherclassical nor canonical co-normal derivatives are well defined. Equivalence ofthe BDIEs to the original BVP, BDIE solvability, solutionuniqueness/non-uniqueness, and as well as Fredholm property and invertibilityof the BDIE operators are analysed in Sobolev (Bessel potential) spaces. It isshown that the BDIE operators for the Neumann BVP are not invertible, andappropriate finite-dimensional perturbations are constructed leading toinvertibility of the perturbed operators.

Analysis of Segregated Boundary-Domain Integral Equations for Variable-Coefficient Dirichlet and Neumann Problems with General Data