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Canavati, Jose A.; Minzoni, Antonmaria A.

A discontinuous Steklov problem with an application to water waves. (English) Zbl 0418.35072

J. Math. Anal. Appl. 69, 540-558 (1979).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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Cited in 22 Documents

MSC:

35R05 PDEs with low regular coefficients and/or low regular data
35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
35J25 Boundary value problems for second-order elliptic equations

Keywords:

discontinuous Steklov problem; second order selfadjoint elliptic; water wave problems; eigenfunction expansions; Green’s function; minimax characterization of the eigenvalues
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References:

[1] Agmon, S.; Douglis, A.; Nirenberg, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I, Comm. Pure Appl. Math., 12, 623-727 (1959) · Zbl 0093.10401
[2] Bramble, J. H.; Osborn, J. E., Approximation of Steklov eigenvalues of non-selfadjoint second order elliptic operators, (Aziz, A. K., The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (1972), Academic Press: Academic Press New York) · Zbl 0264.35055
[3] Coddington, E. A.; Levinson, N., Theory of Ordinary Differential Equations (1955), McGraw-Hill: McGraw-Hill New York · Zbl 0042.32602
[4] Courant, R.; Hilbert, D., (Methods of Mathematical Physics, Vol. 2 (1962), Interscience: Interscience New York) · Zbl 0729.00007
[5] Friedman, A., Partial Differential Equations (1969), Holt, Rinehart & Winston · Zbl 0224.35002
[6] Giraud, G., Généralization des problèmes sur les opérations du type elliptique, Bull. Sci. Math., 56, 316-352 (1932) · JFM 58.0494.02
[7] A. A. Minzoni; A. A. Minzoni
[8] Miranda, C., Partial Differential Equations of Elliptic Type (1970), Springer-Verlag: Springer-Verlag New York · Zbl 0198.14101
[9] Miranda, C., Sul problema misto per le equazioni lineari, ellitiche, Ann. Mat. Pura Appl., 39, 279-303 (1955) · Zbl 0066.34301
[10] Stuart, C. A.; Toland, J. F., A global result applicable to nonlinear Steklov problems, J. Differential Equations, 15, 247-268 (1974) · Zbl 0276.35037
[11] Whitham, G. B.; Minzoni, A. A., On the excitation of edge waves on beaches, J. Fluid Mech., 79, 273-287 (1977) · Zbl 0345.76010
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