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Galerkin finite element methods for semilinear elliptic differential inclusions
1. | Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld |
2. | Institut für Mathematik, Universität Frankfurt, Postfach 111932, D-60054 Frankfurt a.M., Germany |
References:
[1] |
R. A. Adams, "Sobolev Spaces," Academic Press, New York, 1975. |
[2] |
J. Appell and P. P. Zabrejko, "Nonlinear Superposition Operators," 95 of Cambridge Tracts in Mathematics Cambridge University Press, 1990. |
[3] |
J.-P. Aubin and H. Frankowska, "Set-Valued Analysis," Birkhäuser, Boston, 1990. |
[4] |
W.-J. Beyn and J. Rieger, An implicit function theorem for one-sided Lipschitz mappings, Set-Valued and Variational Analysis, 19 (2011), 343-359. |
[5] |
W.-J. Beyn and J. Rieger, The implicit Euler scheme for one-sided Lipschitz differential inclusions, Disc. Cont. Dyn. Sys. B, 14 (2010), 409-428.
doi: 10.3934/dcdsb.2010.14.409. |
[6] |
D. Braess, "Finite Elements," Cambridge University Press, Cambridge, 1997. |
[7] |
S. Carl and D. Motreanu, "Nonsmooth Variational Problems and their Inequalities," Springer, New York, 2007. |
[8] |
T. Donchev, Properties of one sided Lipschitz multivalued maps, Nonlinear Analysis, 49 (2002), 13-20. |
[9] |
L. C. Evans, "Partial Differential Equations," 19 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 1998. |
[10] |
L. Gasiński and N. S. Papageorgiou, "Nonlinear Analysis," 9 of Series in Mathematical Analysis and Applications. Chapman & Hall/CRC, Boca Raton, FL, 2006. |
[11] |
S. Hu and N. S. Papageorgiou, "Handbook of Multivalued Analysis. Vol. II," 500 of Mathematics and its Applications. Kluwer Academic Publishers, Dordrecht, 2000. Applications. |
[12] |
S. Larsson and V. Thomée, "Partial Differential Equations with Numerical Methods," Springer-Verlag, Berlin, 2003. |
[13] |
J. Rieger, Discretizations of linear elliptic partial differential inclusions, Num. Funct. Anal. Opt., 32 (2011), 904-925. |
[14] |
J. Rieger, Implementing Galerkin finite element methods for semilinear elliptic differential inclusions, To appear in Comp. Meth. Appl. Math. |
[15] |
W. Rudin, "Functional Analysis," Mc Graw Hill, Boston, 2003. |
[16] |
V. Thomée, "Galerkin Finite Element Methods for Parabolic Problems," Number 25 in Springer Series in Computational Mathematics. Springer, 2006. |
[17] |
M. Väth, Continuity, compactness, and degree theory for operators in systems involving $p$-Laplacians and inclusions, J. Differential Equations, 245 (2008), 1137-1166. |
[18] | |
[19] |
E. Zeidler., "Nonlinear Functional Analysis and its Applications," volume 2B. Springer, Heidelberg, 1985. |
show all references
References:
[1] |
R. A. Adams, "Sobolev Spaces," Academic Press, New York, 1975. |
[2] |
J. Appell and P. P. Zabrejko, "Nonlinear Superposition Operators," 95 of Cambridge Tracts in Mathematics Cambridge University Press, 1990. |
[3] |
J.-P. Aubin and H. Frankowska, "Set-Valued Analysis," Birkhäuser, Boston, 1990. |
[4] |
W.-J. Beyn and J. Rieger, An implicit function theorem for one-sided Lipschitz mappings, Set-Valued and Variational Analysis, 19 (2011), 343-359. |
[5] |
W.-J. Beyn and J. Rieger, The implicit Euler scheme for one-sided Lipschitz differential inclusions, Disc. Cont. Dyn. Sys. B, 14 (2010), 409-428.
doi: 10.3934/dcdsb.2010.14.409. |
[6] |
D. Braess, "Finite Elements," Cambridge University Press, Cambridge, 1997. |
[7] |
S. Carl and D. Motreanu, "Nonsmooth Variational Problems and their Inequalities," Springer, New York, 2007. |
[8] |
T. Donchev, Properties of one sided Lipschitz multivalued maps, Nonlinear Analysis, 49 (2002), 13-20. |
[9] |
L. C. Evans, "Partial Differential Equations," 19 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 1998. |
[10] |
L. Gasiński and N. S. Papageorgiou, "Nonlinear Analysis," 9 of Series in Mathematical Analysis and Applications. Chapman & Hall/CRC, Boca Raton, FL, 2006. |
[11] |
S. Hu and N. S. Papageorgiou, "Handbook of Multivalued Analysis. Vol. II," 500 of Mathematics and its Applications. Kluwer Academic Publishers, Dordrecht, 2000. Applications. |
[12] |
S. Larsson and V. Thomée, "Partial Differential Equations with Numerical Methods," Springer-Verlag, Berlin, 2003. |
[13] |
J. Rieger, Discretizations of linear elliptic partial differential inclusions, Num. Funct. Anal. Opt., 32 (2011), 904-925. |
[14] |
J. Rieger, Implementing Galerkin finite element methods for semilinear elliptic differential inclusions, To appear in Comp. Meth. Appl. Math. |
[15] |
W. Rudin, "Functional Analysis," Mc Graw Hill, Boston, 2003. |
[16] |
V. Thomée, "Galerkin Finite Element Methods for Parabolic Problems," Number 25 in Springer Series in Computational Mathematics. Springer, 2006. |
[17] |
M. Väth, Continuity, compactness, and degree theory for operators in systems involving $p$-Laplacians and inclusions, J. Differential Equations, 245 (2008), 1137-1166. |
[18] | |
[19] |
E. Zeidler., "Nonlinear Functional Analysis and its Applications," volume 2B. Springer, Heidelberg, 1985. |
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