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A mixed problem for the Laplace equation in a right angle with an oblique derivative given on a side of the angle. (English) Zbl 0289.35024


MSC:

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J25 Boundary value problems for second-order elliptic equations
31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
31A20 Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions
35D10 Regularity of generalized solutions of PDE (MSC2000)
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[1] Avantaggiati, A.; Troisi, M., Spazi di Sobolev con peso e problemi ellittici in un angolo, I, II, III (I: Ann. di Mat. pura e appl., 95, 361-408 (1973) · Zbl 0274.35032
[2] A. Avantaggiati -M. Troisi,Ulteriori contributi allo studio dei problemi ellittici in un angolo, to appear in Ann. di Mat. pura e appl. · Zbl 0297.35023
[3] Barozzi, G. C., Un problema al contorno non omogeneo in un dominio angoloso per equazioni fortemente quasi ellittiche in due variabili, I, II, Rend. Sem. di Mat. Padova, 44, 27-63 (1970) · Zbl 0239.35021
[4] Gandulfo, A., Problèmes aux limites elliptiques dans un domaine plan anguleux, C. R. Acad. Sc. Paris, 269, 836-839 (1969) · Zbl 0213.37101
[5] Grisvard, P., Alternative de Fredholm relative au problème de Dirichlet dans un polygone ou un polyèdre, Boll. Un. Mat. Ital., 5, 4, 132-164 (1972) · Zbl 0277.35035
[6] Hardy -Littlewood -Polya,Inequalities, Cambridge, 1964.
[7] Merigot, M., Régularité des dérivées de la solution du problème de Dirichlet dans un secteur plan, C. R. Acad. Sc. Paris, 273, 356-359 (1971) · Zbl 0217.41203
[8] N. I. Muskhelishvili,Singular integral equations, P. Noordhoff, 1953. · Zbl 0051.33203
[9] Van Ouverkerk, M. P.; Dijkers, Solutions of the equation of Helmholtz in a quarter plane with an oblique boundary condition (1970), Amsterdam: Mathematisch Centrum, Amsterdam · Zbl 0204.11201
[10] G. Talenti,Equazioni di Wiener-Hopf e problemi misti, to appear in Rend. Sem. Mat., Bari. · Zbl 0319.45007
[11] Talenti, G., Sulle equazioni integrali di Wiener-Hopf, Boll. Un. Mat. Ital., 47, suppl. fasc. 1, 18-118 (1973) · Zbl 0281.45007
[12] Talenti, G., Una disuguaglianza concernente equazioni integrali di Wiener-Hopf a nucleo singolare, Rend. Sem. Mat. Fis. Milano, 42, 121-141 (1972) · Zbl 0331.26014 · doi:10.1007/BF02924268
[13] E. C. Titchmarsh,Theory of Fourier integrals, Oxford University Press, 1937. · JFM 63.0367.05
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