no. 3
The dam problem for nonlinear Darcy's laws and Dirichlet boundary conditions
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 26 (1998) no. 3, pp. 453-505 
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     author = {Carrillo, Jos\'e and Lyaghfouri, Abdeslem},
     title = {The dam problem for nonlinear {Darcy's} laws and {Dirichlet} boundary conditions},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {453--505},
     year = {1998},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 26},
     number = {3},
     mrnumber = {1635777},
     zbl = {0928.76111},
     language = {en},
     url = {https://www.numdam.org/item/ASNSP_1998_4_26_3_453_0/}
}
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Carrillo, José; Lyaghfouri, Abdeslem. The dam problem for nonlinear Darcy's laws and Dirichlet boundary conditions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 26 (1998) no. 3, pp. 453-505. https://www.numdam.org/item/ASNSP_1998_4_26_3_453_0/

[Ad] R.A. Adams, "Sobolev Spaces", Academic Press, New York, 1975. | Zbl | MR

[Al1] H.W. Alt, A free boundary problem associated with the flow of ground water, Arch. Rat. Mech. Anal. 64 (1977), 111-126. | Zbl | MR

[Al2] H.W. Alt, Strömunger durch inhomogene poröse Medien mit freiem Rand, J. Reine Angew. Math. 305 (1979), 89-115. | Zbl | MR

[Al3] H.W. AltThe fluid flow through porous media regularity of the free surface, Manuscripta Math. 21 (1977), 255-272. | Zbl | MR

[AC] A Alonso - J.C. Arrillo, A unified formulation for the boundary conditions in some convections-diffusion problems. Proc. European Conference on "Elliptic and Parabolic Problems", Pont-A-Mousson (June 1994) 325, 51-63. Pitman Research Notes in Mathematics. | Zbl

[AG] H.W. Alt - G. Gilardi, The behavior of the free boundary for the dam problem, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 9 (1981), 571-626. | Zbl | MR | Numdam

[AS] N. Ahmed - D.K. Sunada, Nonlinear flow in porous media, J. Hydraulics Div. Proc. Amer. Soc. Civil. Eng. 95 (1969), 1847-1857.

[Ba1] C. Baiocchi, Free boundary problems in the theory of fluid flow through porous media, Proceedings of the International Congress of Mathematicians -Vancouver (1974), 237-243. | Zbl | MR

[Ba2] C. Baiocchi, Free boundary problems in fluid flows through porous media and variational inequalities In: "Free Boundary Problems", Proceedings of a seminar held in Pavia Sept-Oct 1979, Vol. 1 (Roma 1980), pp. 175-191. | Zbl | MR

[BKS] H. Brezis - D. Kinderlehrer - G. Stampacchia, Sur une nouvelle formulation du problème de l'écoulement à travers une digue, C. R. Acad. Sci. Paris Sér. A 287 (1978), 711-714. | Zbl | MR

[Br] H. Brezis, "Analyse Fonctionnelle. Théorie et applications ", Masson, 1987. | Zbl | MR

[C1] J. Carrillo, "An Evolution Free Boundary Problem: Filtrations of a Compressible Fluid in a Porous Medium", Research Notes in Mathematics, Pitman, London, Vol. 89, 1983, pp. 97-110, | Zbl | MR

[C2] J. Carrillo, On the uniqueness of the solution of the evolution dam problem, Nonlinear Anal. Vol. 22, 5 (1994), 573-607. | Zbl | MR

[CC1] J. Carrillo - M. Chipot, On the dam problem, J. Differential Equations 45 (1982), 234-271. | Zbl | MR

[CC2] J. Carrillo - M. Chipot, The dam problem with leaky boundary conditions, Appl. Math. Optim. 28 (1993), 57-85. | Zbl | MR

[CF1] L.A. Caffarelli - A. Friedman, The dam problem with two layers, Arch. Ration. Mech. Anal. 68 (1978), 125-154. | Zbl | MR

[CF2] L.A. Caffarelli - A. Friedman, Asymptotic estimates for the dam problem with several layers, Indiana Univ. Math. J. 27 (1978), 551-580. | Zbl | MR

[CafG] L.A. Caffarelli - G. Gilardi, Monotonicity of the free boundary in the two dimensional dam problem, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 13 (1980), 523-537. | Zbl | MR | Numdam | EuDML

[CarG] J. Carrillo - G. Gilardi, La vitesse de propagation dans le problème de la digue, Ann. Fac. Sci. de Toulouse Math. 11 (1990), 7-28. | Zbl | MR | Numdam | EuDML

[CL1] M. Chipot - A. Lyaghfouri, An existence theorem for an unbounded dam with leaky boundary conditions, Proc. European Conference on "Elliptic and Parabolic Problems", Pont-à-Mousson 325 (June 1994), 64-73. Pitman Research Notes in Mathematics. | Zbl | MR

[CL2] M. Chipot - A. Lyaghfouri, The dam problem for nonlinear Darcy's law and leaky boundary conditions, Math. Methods Appl. Sci. 20 (1997), 1045-1068. | Zbl | MR

[CL3] M. Chipot - A. Lyaghfouri, The dam problem for linear Darcy's law and nonlinear leaky boundary conditions, Advances in Differential Equations, 3 (1998), 1-50. | Zbl | MR

[Dia] J.I. Diaz, "Non Linear Partial Differential Equations and Free Boundaries" Vol I: Elliptic Equations, Pitman Research Notes in Mathematics, London, 1985. | Zbl

[Dib] E. Dibenedetto, C1 local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal. 7 (1983), 827-850. | Zbl | MR

[DB] E. Dibenedetto - A. Friedman, Periodic behaviour for the evolutionary dam problem and related free boundary problems, Comm. Partial Differential Equations 11 (1986), 1297-1377. | Zbl | MR

[Do] Dongming Wei, An existence theorem for weak solution of a nonlinear dam problem, Appl. Anal. 34 (1989), 219-230. | Zbl | MR

[Du] L. Dung, On a class of singular quasilinear elliptic equations with general structures and distributions data, Nonlinear Anal. 28 (1997), 1879-1902. | Zbl | MR

[F] A. Friedman, "Variational Principles and Free-Boundary Problems", Robert E. Krieger Publishing Company, Malabar, Florida, 1988. | Zbl | MR

[FH] A. Friedman - Shav-Yun Huang, The inhomogeneous dam problem with discontinuous permeability, Ann. Scuola. Norm. Sup. Pisa, Cl. Sci (4) 14 (1987), 49-77. | Zbl | MR | Numdam | EuDML

[FT] A. Friedman - A. Torelli, A free boundary problem connected with nonsteady filtration in porous media, Nonlinear Anal. 1 (1977), 503-545. | Zbl | MR

[G] G. Gilardi, A new approach to evolution free boundary problems, Comm. Partial Differential Equations 4 (1979) 1099-1123; 5 (1980), 983-984. | Zbl | MR

[GT] D. Gilbarg - N.S. Trudinger, "Elliptic Partial Differential Equations of Second Order", Springer-Verlag, New York, 1977. | Zbl | MR

[GZ1] R. Gariepy - W.P. Zeimer, Behavior at the boundary of solutions of quasilinear elliptic equations, Arch. Rational. Mech. Anal. 56 (1974), 372-384. | Zbl | MR

[GZ2] R. Gariepy - W.P. Zeimer, A regularity condition at the boundary for solutions of quasilinear elliptic equations, Arch. Rational. Mech. Anal. 67 (1978), 25-39. | Zbl | MR

[HKM] J. Heinonen - T. Kilpeläinen - O. Martio, "Nonlinear Potential Theory of Degenerate Elliptic Equations", Oxford Science Publications, 1993. | Zbl | MR

[K1] T. Kilpeläinen, Hölder continuity of solutions to quasilinear elliptic equations involving measures, Potential Anal. 3 (1994), 265-272. | Zbl | MR

[K2] T. Kilpeläinen, A Rado type theorem for p-harmonic functions in the plane, Electron. J. Differential Equations 9 (1994), approx. 4pp. (electronic). | Zbl | MR | EuDML

[Le1] J.L. Lewis, Regularity of the derivatives of solutions to certain degenerate elliptic equations, Indiana Univ. Math. J. 32 (1983), 849-858. | Zbl | MR

[Le2] J.L. Lewis, Capacitary functions in convex rings, Arch. Rational. Mech. Anal. 66 (1977), 201-224. | Zbl | MR

[Lib] G.M. Liberman, Boundary regularity for solutions of degenerate elliptic equations, Nonlinear Anal. 12 (1988), 1203-1219. | Zbl | MR

[Lio] J.L. Lions, "Quelques méthodes de résolution des problèmes aux limites non linéaires”, Dunod/ Gauthier-Villars, Paris, 1969. | Zbl

[Ly] A. Lyaghfouri, The inhomogeneous dam problem with linear Darcy's law and Dirichlet boundary conditions, Math. Models Methods Appl. Sci. 8 (1996), 1051-1077. | Zbl | MR

[M] J.J. Manfredi, p-harmonicfunctions in the plane, Proc. Amer. Math. Soc. 103, (1988), 473-478. | Zbl | MR

[Ra] J.M. Rakotoson, Equivalence between the growth of ∫ B(x,r) |∇u|Pdy and T in the equation P [u] = T., J. Differential Equations 86 (1990), 102-122. | Zbl

[Ro] J.F. Rodrigues, On the dam problem with leaky boundary condition, Portugal. Math. 39 (1980), 399-411. | Zbl | MR | EuDML

[S] G. Stampacchia, On the filtration of a fluid through a porous medium with variable cross section, Russian Math. Surveys 29 (1974), 89-102. | Zbl | MR

[SV] R. Stavre - B. Vernescu, Incompressible fluid flow through a nonhomogeneous and anistropic dam, Nonlinear Anal. 9 (1985), 799-810. | Zbl | MR

[Tor1] A. Torelli, Existence and uniqueness of the solution of a non steady free boundary problem, Boll. Un. Mat. Ital. (5), 14-B (1977), 423-466. | Zbl | MR

[Tor2] A. Torelli, On a free boundary value problem connected with a non steady filtration phenomenon, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 4 (1977), 33-59. | Zbl | MR | Numdam | EuDML

[Tol] P. Tolksdorf, On the Dirichlet problem for quasilinear equations in domains with conical boundary points, Comm. Partial Differential Equations (7) 8 (1983), 773-817. | Zbl | MR

[V] R.E. Volker, Nonlinear flow in porous media by finite element, J. Hydraulics Div. Proc. Amer. Soc. Civil. Eng. 95 (1969), 2093-2114.