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On the variational $p$-capacity problem in the plane
Time-dependent singularities in the heat equation
1. | Department of Mathematics, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8551, Japan |
2. | Department of Mathematics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551 |
References:
[1] |
H. Brézis and L. Véron, Removable singularities for some nonlinear elliptic equations,, \emph{Arch. Rational Mech. Anal.}, 75 (): 1.
doi: 10.1007/BF00284616. |
[2] |
B. Gidas and J. Spruck, Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math., 34 (1981), 525-598.
doi: 10.1002/cpa.3160340406. |
[3] |
A. Grigor'yan, Heat Kernel and Analysis on Manifolds, American Mathematical Society, Providence, RI, 2009. |
[4] |
K. Hirata, Removable singularities of semilinear parabolic equations, Proc. Amer. Math. Soc., 142 (2014), 157-171.
doi: 10.1090/S0002-9939-2013-11739-9. |
[5] |
S.-Y. Hsu, Removable singularities of semilinear parabolic equations, Adv. Differential Equations, 15 (2010), 137-158. |
[6] |
K. M. Hui, Another proof for the removable singularities of the heat equation, Proc. Amer. Math. Soc., 138 (2010), 2397-2402.
doi: 10.1090/S0002-9939-10-10352-9. |
[7] |
T. Kan and J. Takahashi, On the profile of solutions with time-dependent singularities for the heat equation, Kodai Math. J., 37 (2014), 568-585.
doi: 10.2996/kmj/1414674609. |
[8] |
P.-L. Lions, Isolated singularities in semilinear problems, J. Differential Equations, 38 (1980), 441-450.
doi: 10.1016/0022-0396(80)90018-2. |
[9] |
S. Sato and E. Yanagida, Solutions with moving singularities for a semilinear parabolic equation, J. Differential Equations, 246 (2009), 724-748.
doi: 10.1016/j.jde.2008.09.004. |
[10] |
L. Véron, Singular solutions of some nonlinear elliptic equations, Nonlinear Anal., 5 (1981), 225-242.
doi: 10.1016/0362-546X(81)90028-6. |
[11] |
L. Véron, Singularities of Solutions of Second Order Quasilinear Equations, Longman, Harlow, 1996. |
show all references
References:
[1] |
H. Brézis and L. Véron, Removable singularities for some nonlinear elliptic equations,, \emph{Arch. Rational Mech. Anal.}, 75 (): 1.
doi: 10.1007/BF00284616. |
[2] |
B. Gidas and J. Spruck, Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math., 34 (1981), 525-598.
doi: 10.1002/cpa.3160340406. |
[3] |
A. Grigor'yan, Heat Kernel and Analysis on Manifolds, American Mathematical Society, Providence, RI, 2009. |
[4] |
K. Hirata, Removable singularities of semilinear parabolic equations, Proc. Amer. Math. Soc., 142 (2014), 157-171.
doi: 10.1090/S0002-9939-2013-11739-9. |
[5] |
S.-Y. Hsu, Removable singularities of semilinear parabolic equations, Adv. Differential Equations, 15 (2010), 137-158. |
[6] |
K. M. Hui, Another proof for the removable singularities of the heat equation, Proc. Amer. Math. Soc., 138 (2010), 2397-2402.
doi: 10.1090/S0002-9939-10-10352-9. |
[7] |
T. Kan and J. Takahashi, On the profile of solutions with time-dependent singularities for the heat equation, Kodai Math. J., 37 (2014), 568-585.
doi: 10.2996/kmj/1414674609. |
[8] |
P.-L. Lions, Isolated singularities in semilinear problems, J. Differential Equations, 38 (1980), 441-450.
doi: 10.1016/0022-0396(80)90018-2. |
[9] |
S. Sato and E. Yanagida, Solutions with moving singularities for a semilinear parabolic equation, J. Differential Equations, 246 (2009), 724-748.
doi: 10.1016/j.jde.2008.09.004. |
[10] |
L. Véron, Singular solutions of some nonlinear elliptic equations, Nonlinear Anal., 5 (1981), 225-242.
doi: 10.1016/0362-546X(81)90028-6. |
[11] |
L. Véron, Singularities of Solutions of Second Order Quasilinear Equations, Longman, Harlow, 1996. |
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