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Positive solutions for singular elliptic equations with critical Hardy-Sobolev exponent
A singular limit in a nonlinear problem arising in electromagnetism
| 1. | Technische Universität Berlin, Fakultät II - Mathematik und Naturwissenschaften, Institut für Mathematik, Strasse des 17. Juni 136, 10623 Berlin |
References:
| [1] |
J. M. Ball, Strongly continuous semi groups, weak solutions and the variation of constants formula, Proc. Amer. Math. Soc., 63 (1977), 370-373. |
| [2] |
J. W. Barrett and L. Prigozhin, Bean's critical-state model as the $p\rightarrow\infty$ limit of an evolutionary $p$-Laplace equation, Nonlinear Anal., 42 (2000), 977-993.
doi: doi:10.1016/S0362-546X(99)00147-9. |
| [3] |
C. P. Bean, Magnetization of high-field superconductors, Rev. Mod. Phys., 36 (1964), 31-39.
doi: doi:10.1103/RevModPhys.36.31. |
| [4] |
F. Jochmann, Existence of weak solutions to the drift-diffusion model for semiconductors coupled with Maxwell's equations, J. Math. Anal. Appl., 204 (1996), 655-676.
doi: doi:10.1006/jmaa.1996.0460. |
| [5] |
F. Jochmann, A semi-static limit for Maxwell's equations in an exterior domain, Comm. Part. Diff. Equations, 23 (1998), 2035-2076.
doi: doi:10.1080/03605309808821410. |
| [6] |
F. Jochmann, Regularity of weak solutions to Maxwell's Equations with mixed boundary conditions, Math. Meth. Appl. Sci., 22 (1999), 1255-1274.
doi: doi:10.1002/(SICI)1099-1476(19990925)22:14<1255::AID-MMA83>3.0.CO;2-N. |
| [7] |
F. Jochmann, Energy decay of solutions to Maxwells equations with conductivity and polarization, J. Diff. Equations, 203 (2004), 232-254.
doi: doi:10.1016/j.jde.2004.05.005. |
| [8] |
F. Jochmann, On a first-order hyperbolic systems including Bean's model for superconductors with displacement current, J. Diff. Equations, 246 (2009), 2151-2191.
doi: doi:10.1016/j.jde.2008.12.023. |
| [9] |
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations," 2nd edition, |
| [10] |
R. Picard, An elementary proof for a compact embedding result in generalized electromagnetic theory, Math. Z., 187 (1984), 151-161.
doi: doi:10.1007/BF01161700. |
| [11] |
C. Weber, A local compactness theorem for Maxwell's equations, Math. Methods Appl. Sci., 2 (1980), 12-25.
doi: doi:10.1002/mma.1670020103. |
| [12] |
H. M. Yin, On a $p$-Laplacian type of evolution system and applications to Bean's model in the type-II superconductivity theory, Quarterly. Appl. Math., 59 (2001), 47-66. |
| [13] |
H. M. Yin, On a singular limit problem for nonlinear Maxwell equations, J. Diff. Equations, 156 (1999), 355-375.
doi: doi:10.1006/jdeq.1998.3608. |
| [14] |
H. M. Yin, B. Q. Li and J. Zou, A degenerate evolution system modeling Bean's critical-state type-II superconductors, Discrete Continuous Dynam. Systems - B, 8 (2002), 781-794. |
show all references
References:
| [1] |
J. M. Ball, Strongly continuous semi groups, weak solutions and the variation of constants formula, Proc. Amer. Math. Soc., 63 (1977), 370-373. |
| [2] |
J. W. Barrett and L. Prigozhin, Bean's critical-state model as the $p\rightarrow\infty$ limit of an evolutionary $p$-Laplace equation, Nonlinear Anal., 42 (2000), 977-993.
doi: doi:10.1016/S0362-546X(99)00147-9. |
| [3] |
C. P. Bean, Magnetization of high-field superconductors, Rev. Mod. Phys., 36 (1964), 31-39.
doi: doi:10.1103/RevModPhys.36.31. |
| [4] |
F. Jochmann, Existence of weak solutions to the drift-diffusion model for semiconductors coupled with Maxwell's equations, J. Math. Anal. Appl., 204 (1996), 655-676.
doi: doi:10.1006/jmaa.1996.0460. |
| [5] |
F. Jochmann, A semi-static limit for Maxwell's equations in an exterior domain, Comm. Part. Diff. Equations, 23 (1998), 2035-2076.
doi: doi:10.1080/03605309808821410. |
| [6] |
F. Jochmann, Regularity of weak solutions to Maxwell's Equations with mixed boundary conditions, Math. Meth. Appl. Sci., 22 (1999), 1255-1274.
doi: doi:10.1002/(SICI)1099-1476(19990925)22:14<1255::AID-MMA83>3.0.CO;2-N. |
| [7] |
F. Jochmann, Energy decay of solutions to Maxwells equations with conductivity and polarization, J. Diff. Equations, 203 (2004), 232-254.
doi: doi:10.1016/j.jde.2004.05.005. |
| [8] |
F. Jochmann, On a first-order hyperbolic systems including Bean's model for superconductors with displacement current, J. Diff. Equations, 246 (2009), 2151-2191.
doi: doi:10.1016/j.jde.2008.12.023. |
| [9] |
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations," 2nd edition, |
| [10] |
R. Picard, An elementary proof for a compact embedding result in generalized electromagnetic theory, Math. Z., 187 (1984), 151-161.
doi: doi:10.1007/BF01161700. |
| [11] |
C. Weber, A local compactness theorem for Maxwell's equations, Math. Methods Appl. Sci., 2 (1980), 12-25.
doi: doi:10.1002/mma.1670020103. |
| [12] |
H. M. Yin, On a $p$-Laplacian type of evolution system and applications to Bean's model in the type-II superconductivity theory, Quarterly. Appl. Math., 59 (2001), 47-66. |
| [13] |
H. M. Yin, On a singular limit problem for nonlinear Maxwell equations, J. Diff. Equations, 156 (1999), 355-375.
doi: doi:10.1006/jdeq.1998.3608. |
| [14] |
H. M. Yin, B. Q. Li and J. Zou, A degenerate evolution system modeling Bean's critical-state type-II superconductors, Discrete Continuous Dynam. Systems - B, 8 (2002), 781-794. |
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