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Pointwise estimates of solutions for the multi-dimensional scalar conservation laws with relaxation
A pointwise gradient bound for elliptic equations on compact manifolds with nonnegative Ricci curvature
1. | LAMFA – CNRS UMR 6140, Université de Picardie Jules Verne, 33, rue Saint-Leu 80039 Amiens CEDEX 1, France |
2. | Università degli Studi di Milano, Dipartimento di Matematica Via Saldini, 50, 20133 Milano |
References:
[1] |
Marcel Berger, Paul Gauduchon and Edmond Mazet, "Le Spectre d'une Variété Riemannienne," Lecture Notes in Mathematics, 194, Springer-Verlag, Berlin, 1971. |
[2] |
Luis Caffarelli, Nicola Garofalo and Fausto Segàla, A gradient bound for entire solutions of quasi-linear equations and its consequences, Comm. Pure Appl. Math., 47 (1994), 1457-1473.
doi: 10.1002/cpa.3160471103. |
[3] |
Alberto Farina, Yannick Sire and Enrico Valdinoci, Stable solutions of elliptic equations on Riemannian manifolds, preprint (2008). |
[4] |
Alberto Farina and Enrico Valdinoci, A pointwise gradient estimate in possibly unbounded domains with nonnegative mean curvature, Adv. Math., 225 (2010), 2808-2827.
doi: 10.1016/j.aim.2010.05.008. |
[5] |
David Gilbarg and Neil S. Trudinger, "Elliptic Partial Differential Equations of Second Order," Grundlehren der Mathematischen Wissenschaften, [Fundamental Principles of Mathematical Sciences], 2nd edition, 224, Springer-Verlag, Berlin, 1983. |
[6] |
Luciano Modica, A gradient bound and a Liouville theorem for nonlinear Poisson equations, Comm. Pure Appl. Math., 38 (1985), 679-684.
doi: 10.1002/cpa.3160380515. |
[7] |
L. E. Payne, Some remarks on maximum principles, J. Analyse Math., 30 (1976), 421-433.
doi: 10.1007/BF02786729. |
[8] |
Vladimir E. Shklover, Schiffer problem and isoparametric hypersurfaces, Rev. Mat. Iberoamericana, 16 (2000), 529-569. |
[9] |
René P. Sperb, "Maximum Principles and their Applications," Mathematics in Science and Engineering, 157, Academic Press Inc., New York, 1981. |
[10] |
Gudlaugur Thorbergsson, A survey on isoparametric hypersurfaces and their generalizations, Handbook of Differential Geometry, I, North-Holland, Amsterdam, (2000), 963-995. |
[11] |
show all references
References:
[1] |
Marcel Berger, Paul Gauduchon and Edmond Mazet, "Le Spectre d'une Variété Riemannienne," Lecture Notes in Mathematics, 194, Springer-Verlag, Berlin, 1971. |
[2] |
Luis Caffarelli, Nicola Garofalo and Fausto Segàla, A gradient bound for entire solutions of quasi-linear equations and its consequences, Comm. Pure Appl. Math., 47 (1994), 1457-1473.
doi: 10.1002/cpa.3160471103. |
[3] |
Alberto Farina, Yannick Sire and Enrico Valdinoci, Stable solutions of elliptic equations on Riemannian manifolds, preprint (2008). |
[4] |
Alberto Farina and Enrico Valdinoci, A pointwise gradient estimate in possibly unbounded domains with nonnegative mean curvature, Adv. Math., 225 (2010), 2808-2827.
doi: 10.1016/j.aim.2010.05.008. |
[5] |
David Gilbarg and Neil S. Trudinger, "Elliptic Partial Differential Equations of Second Order," Grundlehren der Mathematischen Wissenschaften, [Fundamental Principles of Mathematical Sciences], 2nd edition, 224, Springer-Verlag, Berlin, 1983. |
[6] |
Luciano Modica, A gradient bound and a Liouville theorem for nonlinear Poisson equations, Comm. Pure Appl. Math., 38 (1985), 679-684.
doi: 10.1002/cpa.3160380515. |
[7] |
L. E. Payne, Some remarks on maximum principles, J. Analyse Math., 30 (1976), 421-433.
doi: 10.1007/BF02786729. |
[8] |
Vladimir E. Shklover, Schiffer problem and isoparametric hypersurfaces, Rev. Mat. Iberoamericana, 16 (2000), 529-569. |
[9] |
René P. Sperb, "Maximum Principles and their Applications," Mathematics in Science and Engineering, 157, Academic Press Inc., New York, 1981. |
[10] |
Gudlaugur Thorbergsson, A survey on isoparametric hypersurfaces and their generalizations, Handbook of Differential Geometry, I, North-Holland, Amsterdam, (2000), 963-995. |
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