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Galerkin finite element methods for semilinear elliptic differential inclusions
1.  Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D33501 Bielefeld 
2.  Institut für Mathematik, Universität Frankfurt, Postfach 111932, D60054 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, "SetValued Analysis," Birkhäuser, Boston, 1990. 
[4] 
W.J. Beyn and J. Rieger, An implicit function theorem for onesided Lipschitz mappings, SetValued and Variational Analysis, 19 (2011), 343359. 
[5] 
W.J. Beyn and J. Rieger, The implicit Euler scheme for onesided Lipschitz differential inclusions, Disc. Cont. Dyn. Sys. B, 14 (2010), 409428. 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), 1320. 
[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," SpringerVerlag, Berlin, 2003. 
[13] 
J. Rieger, Discretizations of linear elliptic partial differential inclusions, Num. Funct. Anal. Opt., 32 (2011), 904925. 
[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), 11371166. 
[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, "SetValued Analysis," Birkhäuser, Boston, 1990. 
[4] 
W.J. Beyn and J. Rieger, An implicit function theorem for onesided Lipschitz mappings, SetValued and Variational Analysis, 19 (2011), 343359. 
[5] 
W.J. Beyn and J. Rieger, The implicit Euler scheme for onesided Lipschitz differential inclusions, Disc. Cont. Dyn. Sys. B, 14 (2010), 409428. 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), 1320. 
[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," SpringerVerlag, Berlin, 2003. 
[13] 
J. Rieger, Discretizations of linear elliptic partial differential inclusions, Num. Funct. Anal. Opt., 32 (2011), 904925. 
[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), 11371166. 
[18]  
[19] 
E. Zeidler., "Nonlinear Functional Analysis and its Applications," volume 2B. Springer, Heidelberg, 1985. 
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