Existence and blow up of solutions to certain classes of two-dimensional nonlinear Neumann problems
Medville, Kai ; Vogelius, Michael S.
Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006), p. 499-538 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_2006__23_4_499_0,
     author = {Medville, Kai and Vogelius, Michael S.},
     title = {Existence and blow up of solutions to certain classes of two-dimensional nonlinear Neumann problems},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {23},
     year = {2006},
     pages = {499-538},
     doi = {10.1016/j.anihpc.2005.02.008},
     mrnumber = {2245754},
     zbl = {05060815},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2006__23_4_499_0}
}

Medville, Kai; Vogelius, Michael S. Existence and blow up of solutions to certain classes of two-dimensional nonlinear Neumann problems. Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) pp. 499-538. doi : 10.1016/j.anihpc.2005.02.008. http://gdmltest.u-ga.fr/item/AIHPC_2006__23_4_499_0/

[1] Ando T., Fowler A.B., Stern F., Electronic properties of two-dimensional system, Rev. Modern Phys. 54 (1982) 437-621.

[2] Bebernes J., Eberly D., Mathematical Problems from Combustion Theory, Appl. Math. Sci., vol. 83, Springer-Verlag, Berlin, 1989. | MR 1012946 | Zbl 0692.35001

[3] Bethuel F., Brezis H., Helein F., Ginzburg-Landau Vortices, Birkhäuser, Boston, 1994. | MR 1269538 | Zbl 0802.35142

[4] Brezis H., Merle F., Uniform estimates and blow-up behavior for solutions of -Δu=Vx0ex0exe u in two dimensions, Comm. Partial Differential Equations 16 (1991) 1223-1253. | MR 1132783 | Zbl 0746.35006

[5] Bryan K., Vogelius M., Singular solutions to a nonlinear elliptic boundary value problem originating from corrosion modeling, Quart. Appl. Math. 60 (2002) 675-694. | MR 1939006 | Zbl 1030.35070

[6] J. Davila, A linear elliptic equation with a nonlinear boundary condition, Preprint, Rutgers University, 2001.

[7] Deconinck J., Current Distributions and Electrode Shape Changes in Electrochemical Systems, Lecture Notes in Engrg., vol. 75, Springer-Verlag, Berlin, 1992.

[8] Jacobsen J., A globalization of the Implicit Function Theorem with applications to nonlinear elliptic equations, Contemp. Math. 289 (2001) 249-272. | MR 1864544 | Zbl 1200.35147 | Zbl 01714734

[9] Kavian O., Introduction à la théorie des points critiques et applications aux problèmes elliptiques, Math. Appl., vol. 13, Springer-Verlag, Berlin, 1993. | MR 1276944 | Zbl 0797.58005

[10] Kavian O., Vogelius M., On the existence and “blow up” of solutions to a two-dimensional nonlinear boundary-value problem arising in corrosion modelling, Proc. Roy. Soc. Edinburgh Sect. A 133 (2003) 119-149, Corrigendum to same, Proc. Roy. Soc. Edinburgh Sect. A 133 (2003) 729-730. | Zbl 1086.35504

[11] K. Medville, Ph.D. Thesis, Rutgers University, 2004.

[12] Medville K., Vogelius M.S., Blow-up behavior of planar harmonic functions satisfying a certain exponential Neumann boundary condition, SIAM J. Math. Anal. 36 (2005) 1772-1806. | MR 2178221 | Zbl 02206097

[13] Nagasaki K., Suzuki T., Asymptotic analysis for two-dimensional elliptic eigenvalue problems with exponentially dominated nonlinearities, Asymptotic Anal. 3 (1990) 173-188. | MR 1061665 | Zbl 0726.35011

[14] Rabinowitz P., Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conf. Ser. in Math., vol. 65, Amer. Math. Soc., Providence, RI, 1986. | MR 845785 | Zbl 0609.58002

[15] Shamma S.E., Asymptotic behavior of Stekloff eigenvalues and eigenfunctions, SIAM J. Appl. Math. 20 (1971) 482-490. | MR 306697 | Zbl 0216.38402

[16] Struwe M., Variational Methods, Ergeb. Math. Grenzgeb., vol. 34, Springer-Verlag, Berlin, 1996. | MR 1411681 | Zbl 0939.49001

[17] Vogelius M., Xu J.-M., A nonlinear elliptic boundary value problem related to corrosion modeling, Quart. Appl. Math. 56 (1998) 479-505. | MR 1637048 | Zbl 0954.35067