An explicit right inverse of the divergence operator which is continuous in weighted norms

• Autorzy: Ricardo G. Durán , Maria Amelia Muschietti
• Języki publikacji: EN

Abstrakty

EN

The existence of a continuous right inverse of the divergence operator in $W₀^{1,p}(Ω)ⁿ$, 1 < p < ∞, is a well known result which is basic in the analysis of the Stokes equations. The object of this paper is to show that the continuity also holds for some weighted norms. Our results are valid for Ω ⊂ ℝⁿ a bounded domain which is star-shaped with respect to a ball B ⊂ Ω. The continuity results are obtained by using an explicit solution of the divergence equation and the classical theory of singular integrals of Calderón and Zygmund together with general results on weighted estimates proven by Stein. The weights considered here are of interest in the analysis of finite element methods. In particular, our result allows us to extend to the three-dimensional case the general results on uniform convergence of finite element approximations of the Stokes equations.

Kategorie tematyczne

• 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
• 35Q30: Navier-Stokes equations
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 148
• Numer: 3
• Strony: 207-219

Daty

wydano

2001

Twórcy

autor

Ricardo G. Durán

• Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, 1644 Victoria, Provincia de Buenos Aires, Argentina

autor

Maria Amelia Muschietti

• Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, Casilla de Correo 172, 1900 La Plata, Provincia de Buenos Aires, Argentina

Identyfikatory

DOI

10.4064/sm148-3-2