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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the time-harmonic scalar wave scattering problems with Dirichlet,Neumann, impedance and transmission boundary conditions. Under this setting, weanalyze how sensitive diffracted fields and Cauchy data are to smallperturbations of a given nominal shape. To this end, we follow [K. Eppler,Int.~J.~Appl. Math. Comput. Sci. 10(3) (2000), pp. 487-516], referred to asexplicit shape calculus, and which places great emphasis on thecharacterization of the domain derivatives as boundary value problems. Itconsists in combining elliptic regularity theorems, shape calculus andfunctional analysis, allowing to deduce sharp differentiability results for thedomain-to-solution and domain-to-Cauchy data mappings. The technique is appliedto both classic and limit Sobolev regularity cases, leading to new andcomprehensive differentiability results.

Shape differentiability of Helmholtz scattering problems via explicit shape calculus