×

Inhomogeneous Orlicz-Sobolev spaces and nonlinear parabolic initial value problems. (English) Zbl 0286.35047


MSC:

35K55 Nonlinear parabolic equations
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47J05 Equations involving nonlinear operators (general)
35G20 Nonlinear higher-order PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aubin, J. P., Un théorème de compacité, C. R. Acad. Sci. Paris, 256, 5042-5044 (1963) · Zbl 0195.13002
[2] Bourbaki, N., Éléments de Mathématique V. Espaces vectoriels topologiques (1956), Hermann: Hermann Paris · Zbl 0067.08302
[3] Browder, F. E., Nonlinear elliptic boundary value problems, Bull. Amer. Math. Soc., 69, 862-874 (1963) · Zbl 0127.31901
[4] Browder, F. E., Problèmes nonlinéaires (1966), Les Presses de l’Université de Montreal · Zbl 0153.17302
[5] F. E. BrowderProc. Symp. in Pure Maths., Amer. Math. Soc.; F. E. BrowderProc. Symp. in Pure Maths., Amer. Math. Soc.
[6] Browder, F. E., Functional Analysis & partial differential equations 1, Math. Ann., 138, 55-79 (1959) · Zbl 0086.10301
[7] Dinculeanu, N., Vector Measures (1967), Pergamon Press: Pergamon Press London
[8] Donaldson, T., Nonlinear elliptic boundary value problems in Orlicz-Sobolev spaces, J. Diff. Eq., 10, 3, 507-528 (1971) · Zbl 0218.35028
[9] Donaldson, T.; Trudinger, N., Orlicz-Sobolev spaces and embedding theorems, J. Functional Analysis, 8, 1, 52-75 (1971) · Zbl 0216.15702
[10] Dunford, N.; Schwartz, J. T., Linear Operators, Part I (1964), Interscience Publishers, Inc: Interscience Publishers, Inc New York
[11] Friedrichs, K. O., The identity of weak and strong extensions of differential operators, Trans. Amer. Math. Soc., 55, 132-151 (1944) · Zbl 0061.26201
[12] Gossez, J. P., Opérateurs monotones non linéaires dans les espaces de Banach non réflexifs, J. Math. Anal. Appl., 34, 2, 371-395 (1971) · Zbl 0228.47040
[13] J. P. Gossez; J. P. Gossez · Zbl 0221.47038
[14] J. P. Gossez; J. P. Gossez · Zbl 0239.35045
[15] Grothendieck, A., Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc., 16 (1955) · Zbl 0064.35501
[16] Krasnoselski, M. A.; Rutitski, V. B., Convex Functions and Orlicz Spaces (1961), Noordhoff: Noordhoff Groningen
[17] Lax, P. D.; Phillips, R. S., Local boundary conditions for dissipative symmetric linear differential operators, Comm. Pure Appl. Math., 13, 427-455 (1960) · Zbl 0094.07502
[18] Luxemburg, W. A.J, Banach function spaces, thesis (1955), Delft · Zbl 0068.09204
[19] Minty, G. J., On a “monotonicity” method for the solution of nonlinear equations in Banach spaces, (Proc. Nat. Acad. Sci. U.S.A., 50 (1963)), 1038-1041 · Zbl 0124.07303
[20] M. RobertC. R. Acad. Sci. Paris275M. RobertC. R. Acad. Sci. Paris275; M. RobertC. R. Acad. Sci. Paris275M. RobertC. R. Acad. Sci. Paris275
[21] Rockafellar, R. T., On the maximal monotonicity of subdifferential mappings, Pac. J. Math., 33, 209-216 (1970) · Zbl 0199.47101
[22] Shaeffer, H. H., Topological Vector Spaces (1966), MacMillan: MacMillan New York
[23] Nakano, S., Generalized modular spaces, Studia Math., 31, 439-449 (1968) · Zbl 0172.39401
[24] Nakano, S., Modulared Semi-ordered Linear Spaces (1950), Tokyo · Zbl 0041.23401
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.