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On the dam problem. (English) Zbl 0504.35082


MSC:

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)
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[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
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[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
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[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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