@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] 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
, and ,[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] 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
, and ,[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] Rapid penetration of a magnetic field into a plasma along an electrode, Sov. J. Plasma Phys., Vol. 16, 1, 1990.
, and ,[9] Electron Magnetohydrodynamics, Physics Reports, Vol. 243, 5, 1994.
, and ,[10] 16, B. B. Kadomtsev (ed), Plenum, New-York, 1990.
, and , Reviews of Plasma Physics, Vol.[11] Linear and quasilinear equations of parabolic type, Transl. Math. Monographs, Vol. 23, Amer. Math. Soc., Providence R.I., 1968. | MR 241822 | Zbl 0174.15403
, and ,[12] 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
and ,[14] A nonlinear oblique derivative boundary value problem for the heat equation, Part II: rapid penetration at the boundary, to appear.
and ,[15] A Problem with an Oblique Derivative for a Quasilinear Parabolic Equation, Zap. Nauch. Sem. S-Peterburg Otdel. Mat. Inst. Steklov (POMI), Vol. 200, 1992.
and ,[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
,