Simultaneous approximation in Lebesgue and Sobolev norms via eigenspaces

Charles L. Fefferman, Karol W. Hajduk, James C. Robinson

Research output: Contribution to journalArticlepeer-review

Abstract

We approximate functions defined on smooth bounded domains by elements of the eigenspaces of the Laplacian or the Stokes operator in such a way that the approximations are bounded and converge in both Sobolev and Lebesgue spaces. We prove an abstract result referred to fractional power spaces of positive, self-adjoint, compact-inverse operators on Hilbert spaces, and then obtain our main result by using the explicit form of these fractional power spaces for the Dirichlet Laplacian and Stokes operators. As a simple application, we prove that all weak solutions of the convective Brinkman–Forchheimer equations posed on a bounded domain in (Formula presented.) satisfy the energy equality.

Original languageEnglish (US)
JournalProceedings of the London Mathematical Society
DOIs
StateAccepted/In press - 2022

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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