Gossez, Jean-Pierre; Mustonen, Vesa Variational inequalities in Orlicz-Sobolev spaces. (English) Zbl 0643.49006 Nonlinear Anal., Theory Methods Appl. 11, 379-392 (1987). Les auteurs étudient l’existence de solutions d’inéquations variationnelles associeés à des opérateurs dont les coefficients ont une croissance non-polynomiale. Ces problèmes sont formulés dans le cadre des espaces de Sobolev-Orlicz. Reviewer: Haïm Brézis (Paris) Cited in 1 ReviewCited in 84 Documents MSC: 35J87 Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators 49J40 Variational inequalities 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 47H05 Monotone operators and generalizations Keywords:existence of solutions; variational inequalities associated to elliptic differential operators; polynomial growth condition; Sobolev-Orlicz spaces; strongly nonlinear problem; operator of monotone type; elliptic boundary value problem × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Adams, R., Sobolev Spaces (1975), Academic Press: Academic Press New York · Zbl 0314.46030 [2] Boccardo, L.; Giachetti, D., Strongly nonlinear unilateral problems, Appl. Math. Optim., 9, 291-301 (1983) · Zbl 0535.49010 [3] Brezis, H., Equations et inéquations non linéaires dans les espaces vectoriels en dualité, Ann. Inst. Fourier, 18, 115-175 (1968) · Zbl 0169.18602 [4] Brezis, H.; Browder, F. E., Strongly nonlinear elliptic boundary value problems, Annali Scu. norm. sup. Pisa, 5, 587-603 (1978) · Zbl 0453.35029 [5] Brezis, H.; Browder, F. E., Some properties of higher order Sobolev spaces, J. Math. pures appl., 61, 245-259 (1982) · Zbl 0512.46034 [6] Browder, F. E., Existence theorems for nonlinear partial differential equations, Proc. Symp. pure Math., Am. Math. Soc., 16, 1-60 (1970) · Zbl 0212.27704 [7] Browder, F. E., Existence theory for boundary value problems for quasilinear elliptic systems with strongly nonlinear lower order terms, Proc. Symp. pure Math., Am. math. Soc., 23, 269-286 (1973) · Zbl 0265.35035 [8] Browder, F. E.; Hess, P., Nonlinear mappings of monotone type in Banach spaces, J. funct. Analysis, 11, 251-294 (1972) · Zbl 0249.47044 [9] Donaldson, T., Nonlinear elliptic boundary value problems in Orlicz-Sobolev spaces, J. diff. Eqns, 10, 507-528 (1971) · Zbl 0218.35028 [10] Donaldson, T.; Trudinger, N. S., Orlicz-Sobolev spaces and imbedding theorems, J. funct. Analysis, 8, 52-75 (1971) · Zbl 0216.15702 [11] Gossez, J.-P., Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients, Trans. Am. math. Soc., 190, 163-205 (1974) · Zbl 0239.35045 [12] Gossez, J.-P., Surjectivity results for pseudo-monotone mappings in complementary systems, J. math. Analysis Applic., 53, 484-494 (1976) · Zbl 0325.47042 [13] Gossez, J.-P., A remark on strongly nonlinear elliptic boundary value problems, Bol. Soc. Bras. Mat., 8, 53-63 (1977) · Zbl 0417.35041 [14] Gossez, J.-P., Some approximation properties in Orlicz-Sobolev spaces, Studia Math., 74, 17-24 (1982) · Zbl 0503.46018 [15] Gossez, J.-P., A strong nonlinear elliptic problem in Orlicz-Sobolev spaces, Proc. Symp. pure Math., Am. Math. Soc., 45, 455-462 (1986) · Zbl 0602.35037 [16] Hess, P., A strongly nonlinear elliptic boundary value problem, J. math. Analysis Applic., 43, 241-249 (1973) · Zbl 0267.35039 [17] Hess, P., On a class of strongly nonlinear elliptic variational inequalities, Math. Annln, 211, 289-297 (1974) · Zbl 0277.49002 [18] Landes, R., On Galerkin’s method in the existence theory for quasilinear elliptic equations, J. funct. Analysis, 39, 123-148 (1980) · Zbl 0452.35037 [19] Landes, R.; Mustonen, V., Pseudo-monotone mappings in Orlicz-Sobolev spaces and nonlinear boundary value problems on unbounded domains, J. math. Analysis Applic., 88, 25-36 (1982) · Zbl 0492.35015 [20] Landes, R.; Mustonen, V., Unilateral obstacle problem for strongly nonlinear second order elliptic operators, Proc. Symp. pure Math., Am. math. Soc., 45, 95-107 (1986) · Zbl 0601.35045 [21] Krasnoselskii, M.; Rutiskii, J., Convex Functions and Orlicz Spaces (1961), Noordhoff: Noordhoff Groningen · Zbl 0095.09103 [22] Lions, J. L., Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires (1969), Dunod: Dunod Paris · Zbl 0189.40603 [23] Webb, J., Boundary value problems for strongly nonlinear elliptic equations, J. Lond. Math. Soc., 21, 123-132 (1980) · Zbl 0438.35029 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.