no. 2
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) no. 2, pp. 221-253 
@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},
     pages = {221--253},
     year = {1999},
     publisher = {Gauthier-Villars},
     volume = {16},
     number = {2},
     mrnumber = {1674770},
     zbl = {0922.35072},
     language = {en},
     url = {https://www.numdam.org/item/AIHPC_1999__16_2_221_0/}
}
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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) no. 2, pp. 221-253. https://www.numdam.org/item/AIHPC_1999__16_2_221_0/

[1] S. Agmon, A. Douglis and L. Nirenberg, 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. | Zbl | MR

[2] H. Amann, Quasilinear Parabolic Systems under Nonlinear Boundary Conditions, Arch. Rat. Mech. Anal., Vol. 92, 1986, pp. 153-191. | Zbl | MR

[3] H. Amann, Parabolic Evolution Equations and Nonlinear Boundary Conditions, J. Diff. Eq., Vol. 72, 1988, pp. 201-269. | Zbl | MR

[4] H. Berestycki, L.A. Caffarelli and L. Nirenberg, Uniform estimates for regularizations of free boundary problems, Analysis and partial differential equations, C. Sadosky & M. Dekker eds., 1990, pp. 567-617. | Zbl

[5] H. Brézis, Analyse Fonctionnelle dans Mathématiques appliquées pour la maîtrise, Masson, 1983. | Zbl | MR

[6] A. Chuvatin, Thèse, Ecole Polytechnique, 1994.

[7] G. Dong, Initial and nonlinear oblique boundary value problems for fully nonlinear parabolic equations, J. Partial Diff. Eq., Vol. 1, 1988, pp. 12-42. | Zbl | MR

[8] A.V. Gordeev, A.V. Grechikha and Y.L. Kalda, Rapid penetration of a magnetic field into a plasma along an electrode, Sov. J. Plasma Phys., Vol. 16, 1, 1990.

[9] A.V. Gordeev, A.S. Kingsep and L.I. Rudakov, Electron Magnetohydrodynamics, Physics Reports, Vol. 243, 5, 1994.

[10] A.S. Kingsep, K.V. Chukbar and V.V. Yan'Kov, Reviews of Plasma Physics, Vol. 16, B. B. Kadomtsev (ed), Plenum, New-York, 1990.

[11] O.A. Ladyženskaja, V.A. Solonnikov and N.N. Ural'Ceva, Linear and quasilinear equations of parabolic type, Transl. Math. Monographs, Vol. 23, Amer. Math. Soc., Providence R.I., 1968. | Zbl | MR

[12] O.A. Ladyženskaja and N.N. Ural'Ceva, Équations aux dérivées partielles de type elliptique, Monogr. Univ. Math., Dunod, Paris, 1968. [13] G. Lieberman and N. Trudinger, Nonlinear oblique boundary value problems for nonlinear elliptic equations, Trans. A.M.S, Vol. 295, 1986, pp. 509-546. | MR

[14] F. Méhats and J.-M. Roquejoffre, A nonlinear oblique derivative boundary value problem for the heat equation, Part II: rapid penetration at the boundary, to appear.

[15] A.I. Nazarov and N.N. Ural'Tseva, 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] D.H. Sattinger, Monotone Methods in Nonlinear Elliptic and Parabolic Boundary Value Problems, Indiana University Mathematics Journal, Vol. 21, n° 11, 1972, pp. 979-1000. | Zbl | MR

[ 17] N.. Trudinger, On Harnack type inequalities and their applications to quasilinear problems, Comm. Pure Appl. Math., Vol. 20, 1967, pp. 721-747. | Zbl | MR