On the dam problem. (English) Zbl 0504.35082


35R35 Free boundary problems for PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
76S05 Flows in porous media; filtration; seepage
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
Full Text: DOI


[1] Alt, H.W, A free boundary problem associated with the flow of ground water, Arch. rat. mech. anal., 64, 111-126, (1977) · Zbl 0371.76079
[2] Alt, H.W, The fluid flow through porous media. regularity of the free surface, Manuscripta math., 21, 255-272, (1977) · Zbl 0371.76080
[3] Alt, H.W, Strömungen durch inhomogene poröse medien mit freiem rand, J. reine angew. math., 305, 89-115, (1979) · Zbl 0392.76091
[4] Baiocchi, C, Su un problema di frontiera libera connesso a questioni di idraulica, Ann. mat. pura appl., 92, 107-127, (1972) · Zbl 0258.76069
[5] Baiocchi, C, Free boundary problems in the theory of fluid flow through porous media, (), 237-243
[6] Baiocchi, C, Free boundary problems in fluid flow through porous media and variational inequalities, (), 175-191, Rome · Zbl 0481.76100
[7] Baiocchi, C; Capelo, A, ()
[8] Brezis, H; Kinderlehrer, D; Stampacchia, G, Sur une nouvelle formulation du problème de l’écoulement à travers une digue, C. R. acad. sci. Paris Sér. A, 287, 711-714, (1978) · Zbl 0391.76072
[9] Caffarelli, L.A; Gilardi, G, Monotonicity of the free boundary in the two-dimensional dam problem, Anal. scol. norm. sup. Pisa, 7, 523-537, (1980) · Zbl 0513.76090
[10] Friedman, A; Jensen, R, Convexity of the free boundary in the Stefan problem and in the dam problem, Arch. rat. mech. anal., 67, 1-24, (1978) · Zbl 0375.35028
[11] Gilbarg, D; Trudinger, N.S, Elliptic partial differential equations of second order, (1977), Springer-Verlag New York · Zbl 0691.35001
[12] Schwartz, L, Théorie des distributions, (1966), Hermann Paris
[13] Visintin, A, Study of a free boundary filtration problem by a nonlinear variational equation, Boll. un. mat. ital., 5, 212-237, (1979) · Zbl 0405.76061
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