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Durana, R.; Muschietti, M.-A.; Russ, E.; Tchamitchian, P. "Divergence operator and Poincaré inequalities on arbitrary bounded domainsy" (2010) Complex Variables and Elliptic Equations. 55(8):795-816
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Abstract:

Let Ω be an arbitrary bounded domain of ℝn. We study the right invertibility of the divergence on Ω in weighted Lebesgue and Sobolev spaces on Ω, and rely this invertibility to a geometric characterization of Ω and to weighted Poincaré inequalities on Ω. We recover, in particular, well-known results on the right invertibility of the divergence in Sobolev spaces when Ω is Lipschitz or, more generally, when Ω is a John domain, and focus on the case of s-John domains. © 2010 Taylor & Francis.

Registro:

Documento: Artículo
Título:Divergence operator and Poincaré inequalities on arbitrary bounded domainsy
Autor:Durana, R.; Muschietti, M.-A.; Russ, E.; Tchamitchian, P.
Filiación:Facultad de Ciencias Exactas y Naturales, Departmento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, (1428) Buenos Aires, Argentina
Facultad de Ciencias Exactas, Departamento de Matemática, Universidad Nacional de La Plata, Casilla de Correo 172, 1900 La Plata, Provincia de Buenos Aires, Argentina
Faculté des Sciences et Techniques, Université Paul Cézanne, CNRS, LATP (UMR 6632), Case cour A, Avenue Escadrille Normandie-Niemen, F-13397 Marseille Cedex 20, France
Palabras clave:Divergence; Geodesic distance; Inequalities; Poincaré
Año:2010
Volumen:55
Número:8
Página de inicio:795
Página de fin:816
DOI: http://dx.doi.org/10.1080/17476931003786659
Título revista:Complex Variables and Elliptic Equations
Título revista abreviado:Complex Var. Elliptic Equ.
ISSN:17476933
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17476933_v55_n8_p795_Durana

Referencias:

  • Brenner, S.C., Scott, L.R., (1994) The Mathematical Theory of Finite Elements Methods, , Springer, Berlin
  • Auscher, P., Russ, E., Tchamitchian, P., Hardy Sobolev spaces on strongly Lipschitz domains of Rn (2005) J. Funct. Anal, 218, pp. 54-109
  • Dacorogna, B., Fusco, N., Tartar, L., On the solvability of the equation divu 1/4f in L1 and in C0 (2003) Rend. Mat. Acc. Lincei, 9 (3-14), pp. 239-245
  • McMullen, C.T., Lipschitz maps and nets in Euclidean space (1998) Geom. Funct. Anal, 8, pp. 304-314
  • Necas, J., Les Méthodes Directes en Théorie des Équations Elliptiques (1967) Masson Et Cie, Paris; Academia, Editeurs, Prague
  • Bourgain, J., Brezis, H., On the equation divY1/4f and application to control of phases (2003) J. Amer. Math. Soc, 16 (2), pp. 393-426
  • Babuska, I., Aziz, A.K., Survey lectures on the mathematical foundation of the finite element method (1972) The Mathematical Foundations of The Finite Element Method With Applications to Partial Differential Equations, pp. 535-539. , A.K. Aziz, ed., Academic Press, New York
  • Girault, V., Raviart, P.A., (1986) Finite Element Methods For Navier-Stokes Equations, , Springer, Berlin
  • Ladyzhenskaya, O.A., (1969) The Mathematical Theory of Viscous Incompressible Flow, , Gordon and Breach, New York
  • Arnold, D.N., Scott, L.R., Vogelius, M., Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon (1988) Ann. Scuol. Norm. Sup. Pisa, 15, pp. 169-192
  • Bogovskii, M.E., Solution of the first boundary value problem for the equation of continuity of an incompressible medium (1979) Sov. Math. Dokl, 20, pp. 1094-1098
  • Duran, R.G., Muschietti, M.A., An explicit right inverse of the divergence operator which is continuous in weighted norms (2001) Stud. Math, 148 (3), pp. 207-219
  • Acosta, G., Duran, R., Muschietti, M.A., Solutions of the divergence operator on John domains (2006) Adv. Math, 206 (2), pp. 373-401
  • Duran, R., Garcia, F.L., Solutions of the divergence and analysis of the Stokes equations in planar Hölder-alpha domains (2010) Math Models Methods Appl. Sci, 20 (1), pp. 95-120
  • Hajlasz, P., Koskela, P., Sobolev met Poincaré (2000) Mem. AMS, p. 145
  • Diening, L., Ruzicka, M., Schumacher, K., A decomposition technique for John domains (2010) Ann. Acad. Sci. Fen. Math, 35, pp. 87-114
  • Drelichman, I., Duran, R., Improved Poincaré inequalities with weights (2008) J. Math. Anal. Appl, 347, pp. 286-293
  • Hajlasz, P., Koskela, P., Isoperimetric inequalities and imbedding theorems in irregular domains (1998) J. Lond. Math. Soc, 58 (2), pp. 425-450
  • Boas, H.P., Straube, E.J., Integral inequalities of Hardy and Poincaré type (1988) Proc. Amer. Math. Soc, 103 (1), pp. 172-176

Citas:

---------- APA ----------
Durana, R., Muschietti, M.-A., Russ, E. & Tchamitchian, P. (2010) . Divergence operator and Poincaré inequalities on arbitrary bounded domainsy. Complex Variables and Elliptic Equations, 55(8), 795-816.
http://dx.doi.org/10.1080/17476931003786659
---------- CHICAGO ----------
Durana, R., Muschietti, M.-A., Russ, E., Tchamitchian, P. "Divergence operator and Poincaré inequalities on arbitrary bounded domainsy" . Complex Variables and Elliptic Equations 55, no. 8 (2010) : 795-816.
http://dx.doi.org/10.1080/17476931003786659
---------- MLA ----------
Durana, R., Muschietti, M.-A., Russ, E., Tchamitchian, P. "Divergence operator and Poincaré inequalities on arbitrary bounded domainsy" . Complex Variables and Elliptic Equations, vol. 55, no. 8, 2010, pp. 795-816.
http://dx.doi.org/10.1080/17476931003786659
---------- VANCOUVER ----------
Durana, R., Muschietti, M.-A., Russ, E., Tchamitchian, P. Divergence operator and Poincaré inequalities on arbitrary bounded domainsy. Complex Var. Elliptic Equ. 2010;55(8):795-816.
http://dx.doi.org/10.1080/17476931003786659