Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 15 (1988) no. 2, pp. 169-192. 
@article{ASNSP_1988_4_15_2_169_0,
     author = {Arnold, Douglas N. and Scott, L. Ridgway and Vogelius, Michael},
     title = {Regular inversion of the divergence operator with {Dirichlet} boundary conditions on a polygon},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {169--192},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 15},
     number = {2},
     year = {1988},
     mrnumber = {1007396},
     zbl = {0702.35208},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1988_4_15_2_169_0/}
}
TY  - JOUR
AU  - Arnold, Douglas N.
AU  - Scott, L. Ridgway
AU  - Vogelius, Michael
TI  - Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1988
SP  - 169
EP  - 192
VL  - 15
IS  - 2
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_1988_4_15_2_169_0/
LA  - en
ID  - ASNSP_1988_4_15_2_169_0
ER  - 
%0 Journal Article
%A Arnold, Douglas N.
%A Scott, L. Ridgway
%A Vogelius, Michael
%T Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1988
%P 169-192
%V 15
%N 2
%I Scuola normale superiore
%U http://www.numdam.org/item/ASNSP_1988_4_15_2_169_0/
%G en
%F ASNSP_1988_4_15_2_169_0
Arnold, Douglas N.; Scott, L. Ridgway; Vogelius, Michael. Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 15 (1988) no. 2, pp. 169-192. http://www.numdam.org/item/ASNSP_1988_4_15_2_169_0/

[1] R.A. Adams, Sobolev Spaces, Academic Press, New York, NY, 1975. | MR | Zbl

[2] D.N. Arnold - F. Brezzi - J. Douglas, PEERS: A new mixed finite element for plane elasticity, Japan J. Appl. Math., 1 (1984), pp. 347-367. | MR | Zbl

[3] P. Grisvard, Elliptic Problems in Nonsmooth Domains, Pitman, Marshfield, MA, 1985. | MR | Zbl

[4] G.N. Jakovlev, Traces of functions in the space Wl p on piecewise smooth surfaces, Mat. Sb. (N.S.), 74 (1967). Math. USSR-Sb., 3 (1967), pp. 481-497. | MR | Zbl

[5] J.L. Lions - E. Magenes, Non-homogeneous Boundary Value Problems and Applications, I, Springer-Verlag, New York-Heidelberg -Berlin, 1972. | Zbl

[6] M. Morley, A family of mixed elements for linear elasticity, Univ. of Chicago, PhD Thesis, 1986.

[7] J Nečas, Les Méthodes Directes en Théorie des Équations Elliptiques, Masson et Cie., Paris, 1967. | MR

[8] L.R. Scott - M. Vogelius, Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials, Math. Modelling and Numer. Anal., 19 (1985), pp. 111-143. | Numdam | MR | Zbl

[9] K.T. Smith, A Primer of Modern Analysis, Springer-Verlag, New York-Heidelberg-Berlin, 1983. | MR | Zbl

[10] E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970. | MR | Zbl