@article{AIHPC_1999__16_2_221_0,
author = {Mehats, Florian and Roquejoffre, Jean-Michel},
title = {A nonlinear oblique derivative boundary value problem for the heat equation. Part 1 : basic results},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
volume = {16},
year = {1999},
pages = {221-253},
mrnumber = {1674770},
zbl = {0922.35072},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPC_1999__16_2_221_0}
}
Mehats, Florian; Roquejoffre, Jean-Michel. A nonlinear oblique derivative boundary value problem for the heat equation. Part 1 : basic results. Annales de l'I.H.P. Analyse non linéaire, Tome 16 (1999) pp. 221-253. http://gdmltest.u-ga.fr/item/AIHPC_1999__16_2_221_0/
[1] , and , Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I and II, Comm. Pure Appl. Math., Vol. 12, 1959, pp. 623-727; Vol. 17, 1964, pp. 35-92. | MR 162050 | Zbl 0093.10401
[2] , Quasilinear Parabolic Systems under Nonlinear Boundary Conditions, Arch. Rat. Mech. Anal., Vol. 92, 1986, pp. 153-191. | MR 816618 | Zbl 0596.35061
[3] , Parabolic Evolution Equations and Nonlinear Boundary Conditions, J. Diff. Eq., Vol. 72, 1988, pp. 201-269. | MR 932367 | Zbl 0658.34011
[4] , and , Uniform estimates for regularizations of free boundary problems, Analysis and partial differential equations, C. Sadosky & M. Dekker eds., 1990, pp. 567-617. | Zbl 0702.35252
[5] , Analyse Fonctionnelle dans Mathématiques appliquées pour la maîtrise, Masson, 1983. | MR 697382 | Zbl 0511.46001
[6] , Thèse, Ecole Polytechnique, 1994.
[7] , Initial and nonlinear oblique boundary value problems for fully nonlinear parabolic equations, J. Partial Diff. Eq., Vol. 1, 1988, pp. 12-42. | MR 985445 | Zbl 0699.35152
[8] , and , Rapid penetration of a magnetic field into a plasma along an electrode, Sov. J. Plasma Phys., Vol. 16, 1, 1990.
[9] , and , Electron Magnetohydrodynamics, Physics Reports, Vol. 243, 5, 1994.
[10] , and , Reviews of Plasma Physics, Vol. 16, B. B. Kadomtsev (ed), Plenum, New-York, 1990.
[11] , and , Linear and quasilinear equations of parabolic type, Transl. Math. Monographs, Vol. 23, Amer. Math. Soc., Providence R.I., 1968. | MR 241822 | Zbl 0174.15403
[12] and , Équations aux dérivées partielles de type elliptique, Monogr. Univ. Math., Dunod, Paris, 1968. [13] and , Nonlinear oblique boundary value problems for nonlinear elliptic equations, Trans. A.M.S, Vol. 295, 1986, pp. 509-546. | MR 239273
[14] and , A nonlinear oblique derivative boundary value problem for the heat equation, Part II: rapid penetration at the boundary, to appear.
[15] and , A Problem with an Oblique Derivative for a Quasilinear Parabolic Equation, Zap. Nauch. Sem. S-Peterburg Otdel. Mat. Inst. Steklov (POMI), Vol. 200, 1992.
[16] , Monotone Methods in Nonlinear Elliptic and Parabolic Boundary Value Problems, Indiana University Mathematics Journal, Vol. 21, n° 11, 1972, pp. 979-1000. | MR 299921 | Zbl 0223.35038
[ 17] , On Harnack type inequalities and their applications to quasilinear problems, Comm. Pure Appl. Math., Vol. 20, 1967, pp. 721-747. | MR 226198 | Zbl 0153.42703