On asymptotically optimal cubatures for multidimensional Sobolev spaces

V.F. Babenko; Yu.V. Babenko; O.V. Kovalenko

doi:10.15421/242106

On asymptotically optimal cubatures for multidimensional Sobolev spaces

V.F. Babenko (Oles Honchar Dnipro National University), https://orcid.org/0000-0001-6677-1914
Yu.V. Babenko (Kennesaw State University)
O.V. Kovalenko (Oles Honchar Dnipro National University), https://orcid.org/0000-0002-0446-1125

Abstract

We find an asymptotically optimal method of recovery of the weighted integral for the classes of multivariate functions that are defined via restrictions on their (distributional) gradient.

Keywords

asymptotically optimal recovery methods; weighted cubature formulae; multidimensional Sobolev space

MSC 2020

41A55; 41A44; 26D10

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References

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