Simultaneous approximation in Lebesgue and Sobolev norms via eigenspaces

2022/07/10 by Charles Fefferman, Charles L. Fefferman, Karol W. Hajduk +1 · 1 citation
Mathematics · #Numerical methods in inverse problems #Differential Equations and Boundary Problems #Navier-Stokes equation solutions

paper · pdf · doi:10.1112/plms.12469

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

Citations

• The Multiplier Problem for the Ball

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