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Steiner symmetrization for concave semilinear elliptic and parabolic equations and the obstacle problem
1. | Instituto de Matemática Interdisciplinar and Dpto. de Matemática Aplicada, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de las Ciencias, 3, 28040 Madrid, Spain, Spain |
References:
[1] |
A. Alvino, J.I. Díaz, P.L. Lions and G.Trombetti, Elliptic Equations and Steiner Symmetrization,, Communications on Pure and Applied Mathematics, (1996), 217. Google Scholar |
[2] |
H. Attouch, H. and A. Damlamian, Problemes d'evolution dans les Hilbert et applications,, J. Math. Pures Appl., 54 (1975), 53. Google Scholar |
[3] |
C. Bandle, Isoperimetric Inequalities and Applications,, Pitman, (1980). Google Scholar |
[4] |
P. Benilan, M. Crandall and A. Pazy, Nonlinear evolution equations in Banach spaces., Book in preparation., (). Google Scholar |
[5] |
H. Brezis, Operateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert., Notes de Matematica, (1973). Google Scholar |
[6] |
H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations,, Springer, (2010). Google Scholar |
[7] |
F. Chiacchio and V.M. Monetti, Comparison results for solutions of elliptic problems via Steiner symmetrization., Differential and Integral Equations 14(11) (2001), 14 (2001), 1351. Google Scholar |
[8] |
F. Chiacchio, Steiner symmetrization for an elliptic problem with lower-order terms., Ricerche di Matematica, 53 (2004), 87. Google Scholar |
[9] |
F. Chiacchio, Estimates for the first eigenfunction of linear eigenvalue problems via Steiner symmetrization,, Publ. Mat., 1 (2009), 47. Google Scholar |
[10] |
J. I. Díaz, Nonlinear Partial Differential Equations and Free Boundaries., Pitman, (1985). Google Scholar |
[11] |
J.I. Díaz, Simetrización de problemas parablicos no lineales: Aplicación a ecuaciones de reacción difusión., Memorias de la Real Acad. de Ciencias Exactas, (1991). Google Scholar |
[12] |
J.I. Díaz and D. Gómez-Castro, On the effectiveness of wastewater cylindrical reactors: an analysis through Steiner symmetrization., Pure and Applied Geophysics. DOI: 10.1007/s00024-015-1124-8 (2015)., (2015), 00024. Google Scholar |
[13] |
V. Ferone and A. Mercaldo, A second order derivation formula for functions defined by integrals,, C.R. Acad. Sci. Paris, 236 (1998), 549. Google Scholar |
[14] |
J. Mossino, and J.M. Rakotoson, Isoperimetric inequalities in parabolic equations,, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 13 (1986), 51. Google Scholar |
[15] |
T. Nagai, Global existence and decay estimates of solutions to a parabolic-elliptic system of drift-diffusion type in $\mathbb{ R}^{2}$,, Differential Integral Equations 24(1/2) (2011), 24 (2011), 29. Google Scholar |
[16] |
P.-A. Vuillermot, W.F. Wreszinski and V.A.Zagrebnov, A Trotter-Kato Product Formula for a Class of Non-Autonomous Evolution Equations,, Trends in Nonlinear Analysis: in Honour of Professor V. Lakshmikantham, 69 (2008), 1067. Google Scholar |
show all references
References:
[1] |
A. Alvino, J.I. Díaz, P.L. Lions and G.Trombetti, Elliptic Equations and Steiner Symmetrization,, Communications on Pure and Applied Mathematics, (1996), 217. Google Scholar |
[2] |
H. Attouch, H. and A. Damlamian, Problemes d'evolution dans les Hilbert et applications,, J. Math. Pures Appl., 54 (1975), 53. Google Scholar |
[3] |
C. Bandle, Isoperimetric Inequalities and Applications,, Pitman, (1980). Google Scholar |
[4] |
P. Benilan, M. Crandall and A. Pazy, Nonlinear evolution equations in Banach spaces., Book in preparation., (). Google Scholar |
[5] |
H. Brezis, Operateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert., Notes de Matematica, (1973). Google Scholar |
[6] |
H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations,, Springer, (2010). Google Scholar |
[7] |
F. Chiacchio and V.M. Monetti, Comparison results for solutions of elliptic problems via Steiner symmetrization., Differential and Integral Equations 14(11) (2001), 14 (2001), 1351. Google Scholar |
[8] |
F. Chiacchio, Steiner symmetrization for an elliptic problem with lower-order terms., Ricerche di Matematica, 53 (2004), 87. Google Scholar |
[9] |
F. Chiacchio, Estimates for the first eigenfunction of linear eigenvalue problems via Steiner symmetrization,, Publ. Mat., 1 (2009), 47. Google Scholar |
[10] |
J. I. Díaz, Nonlinear Partial Differential Equations and Free Boundaries., Pitman, (1985). Google Scholar |
[11] |
J.I. Díaz, Simetrización de problemas parablicos no lineales: Aplicación a ecuaciones de reacción difusión., Memorias de la Real Acad. de Ciencias Exactas, (1991). Google Scholar |
[12] |
J.I. Díaz and D. Gómez-Castro, On the effectiveness of wastewater cylindrical reactors: an analysis through Steiner symmetrization., Pure and Applied Geophysics. DOI: 10.1007/s00024-015-1124-8 (2015)., (2015), 00024. Google Scholar |
[13] |
V. Ferone and A. Mercaldo, A second order derivation formula for functions defined by integrals,, C.R. Acad. Sci. Paris, 236 (1998), 549. Google Scholar |
[14] |
J. Mossino, and J.M. Rakotoson, Isoperimetric inequalities in parabolic equations,, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 13 (1986), 51. Google Scholar |
[15] |
T. Nagai, Global existence and decay estimates of solutions to a parabolic-elliptic system of drift-diffusion type in $\mathbb{ R}^{2}$,, Differential Integral Equations 24(1/2) (2011), 24 (2011), 29. Google Scholar |
[16] |
P.-A. Vuillermot, W.F. Wreszinski and V.A.Zagrebnov, A Trotter-Kato Product Formula for a Class of Non-Autonomous Evolution Equations,, Trends in Nonlinear Analysis: in Honour of Professor V. Lakshmikantham, 69 (2008), 1067. Google Scholar |
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