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The conormal derivative problem for elliptic equations of variational type. (English) Zbl 0476.35032


MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35B45 A priori estimates in context of PDEs
35A15 Variational methods applied to PDEs
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[1] Concus, P.; Finn, R., On capillary free surfaces in a gravitational field, Acta Math., 132, 207-223 (1974) · Zbl 0382.76005
[2] Finn, R.; Gerhardt, C., The internal sphere condition and the capillary problem, Ann. Mat. Pura Appl., 112, 13-31 (1977) · Zbl 0349.49019
[3] Fiorenza, R., Sui problemi di derivata obliqua per le equazioni ellitiche, Ricerche Mat., 8, 83-110 (1959) · Zbl 0090.31404
[4] Gerhardt, C., Hypersurfaces of prescribed mean curvature over obstacles, Math. Z., 133, 169-185 (1973) · Zbl 0265.35027
[5] Gerhardt, C., Global regularity of the solutions to the capillarity problem, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 3, 157-176 (1976), (4) · Zbl 0338.49008
[6] Gilbarg, D.; Hőrmander, L., Intermediate Schauder estimates, Arch. Rational Mech. Anal., 74, 297-318 (1980) · Zbl 0454.35022
[7] Gilbarg, D.; Trudinger, N. S., Elliptic Partial Differential Equations of Second Order (1977), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York · Zbl 0691.35001
[8] Ladyzenskaja, O. A.; Solonnikov, V. A.; Ural’ceva, N. N., Linear and Quasilinear Equations of Parabolic Type (1968), Amer. Math. Soc: Amer. Math. Soc Providence, R. I, (English translation from Russian)
[9] Ladyzhenskaya, O. A.; Ural’tseva, N. N., Linear and Quasilinear Elliptic Equations (1968), Academic Press: Academic Press New York, (English translation from Russian) · Zbl 0164.13002
[10] Lieberman, G. M., The quasilinear Dirichlet problem with decreased regularity at the boundary, Comm. Partial Differential Equations, 6, 437-497 (1981) · Zbl 0458.35039
[11] Lieberman, G. M., Solvability of quasilinear elliptic equations with nonlinear boundary conditions, Trans. Amer. Math. Soc., 273, 753-765 (1982) · Zbl 0498.35039
[12] G. M. Lieberman, Interior gradient estimates for non-uniformly parabolic equations, Indiana Univ. Math. J.; G. M. Lieberman, Interior gradient estimates for non-uniformly parabolic equations, Indiana Univ. Math. J. · Zbl 0491.35021
[13] Moser, J., A new proof of De Giorgi’s theorem concerning the regularity problem for elliptic differential equations, Comm. Pure Appl. Math., 13, 457-468 (1960) · Zbl 0111.09301
[14] Simon, L., Interior gradient bounds for non-uniformly elliptic equations, Indiana Univ. Math. J., 25, 821-855 (1976) · Zbl 0346.35016
[15] Simon, L. M.; Spruck, J., Existence and regularity of a capillary surface with prescribed contact angle, Arch. Rational Mech. Anal., 61, 19-34 (1976) · Zbl 0361.35014
[16] Spruck, J., On the existence of a capillary surface with prescribed contact angle, Comm. Pure Appl. Math., 28, 189-200 (1975) · Zbl 0297.76018
[17] Trudinger, N. S., On Harnack type inequalities and their applications to quasilinear elliptic partial differential equations, Comm. Pure Appl. Math., 20, 721-747 (1967) · Zbl 0153.42703
[18] Ural’ceva, N. N., Solvability of the capillary problem, Vestnik Leningrad Univ. Math., 6, 363-375 (1979), (English translation from Russian) · Zbl 0419.35040
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