Some results in the theory of Orlicz spaces and applications to variational problems
- Nonlinear Analysis, Function Spaces and Applications, Publisher: Czech Academy of Sciences, Mathematical Institute(Praha), page 50-92
Access Full Article
topHow to cite
topCianchi, Andrea. "Some results in the theory of Orlicz spaces and applications to variational problems." Nonlinear Analysis, Function Spaces and Applications. Praha: Czech Academy of Sciences, Mathematical Institute, 1999. 50-92. <http://eudml.org/doc/220009>.
@inProceedings{Cianchi1999,
author = {Cianchi, Andrea},
booktitle = {Nonlinear Analysis, Function Spaces and Applications},
keywords = {Spring school; Proceedings; Nonlinear analysis; Function spaces; Prague (Czech Republic)},
location = {Praha},
pages = {50-92},
publisher = {Czech Academy of Sciences, Mathematical Institute},
title = {Some results in the theory of Orlicz spaces and applications to variational problems},
url = {http://eudml.org/doc/220009},
year = {1999},
}
TY - CLSWK
AU - Cianchi, Andrea
TI - Some results in the theory of Orlicz spaces and applications to variational problems
T2 - Nonlinear Analysis, Function Spaces and Applications
PY - 1999
CY - Praha
PB - Czech Academy of Sciences, Mathematical Institute
SP - 50
EP - 92
KW - Spring school; Proceedings; Nonlinear analysis; Function spaces; Prague (Czech Republic)
UR - http://eudml.org/doc/220009
ER -
References
top- Adams R. A., Sobolev spaces, Academic Press, New York 1975. (1975) Zbl0314.46030MR0450957
- Adams R. A., On the Orlicz-Sobolev imbedding theorem, J. Funct. Anal. 24 (1977), 241–257. (1977) Zbl0344.46077MR0430770
- Bennett C., Rudnick K., On Lorentz-Zygmund spaces, Dissertationes Mathematicae, CLXXV, Warszawa 1980. (1980) Zbl0456.46028MR0576995
- Bennett C., Sharpley R., Interpolation of operators, Pure and Applied Mathematics, Vol. 129, Academic Press, Boston 1988. (1988) Zbl0647.46057MR0928802
- Bhattacharya T., Leonetti F., A new Poincaré inequality and its applications to the regularity of minimizers of integral functionals with nonstandard growth, Nonlinear Anal. 17 (1991), 833–839. (1991) MR1131493
- Bloom S., Kerman R., Weighted integral inequalities for operators of Hardy type, Studia Math. 110 (1994), 35–52. (1994) MR1279373
- Brothers J. E., Ziemer W. P., Minimal rearrangements of Sobolev functions, J. Reine Angew. Math. 384 (1988), 153–179. (1988) Zbl0633.46030MR0929981
- Calderón A. P., Spaces between and and the theorem of Marcinkiewicz, Studia Math. 26 (1966), 273–299. (1966) MR0203444
- Cianchi A., On relative isoperimetric inequalities in the plane, Boll. Un. Mat. Ital. (7) 3-B (1989), 289–325. (1989) Zbl0674.49030MR0997998
- Cianchi A., Continuity properties of functions from Orlicz-Sobolev spaces and embedding theorems, Ann. Scuola Norm. Sup. Pisa. Cl. Sci. (4) 23 (1996), 575–608. (1996) Zbl0877.46023MR1440034
- Cianchi A., A sharp embedding theorem for Orlicz–Sobolev spaces, Indiana Univ. Math. J. 45 (1996), 39–65. (1996) Zbl0860.46022MR1406683
- Cianchi A., Strong and weak type inequalities for some classical operators in Orlicz spaces, To appear in J. London Math. Soc. Zbl0940.46015MR1721824
- Cianchi A., Hardy inequalities in Orlicz spaces, To appear in Trans. Amer. Math. Soc. Zbl0920.46021MR1433113
- Cianchi A., Boundedness of solutions to variational problems under general growth conditions, Comm. Partial Differential Equations 22 (1997), 1629–1646. (1997) Zbl0892.35048MR1469584
- Cianchi A., An optimal interpolation theorem of Marcinkiewicz type in Orlicz spaces, J. Funct. Anal. 153 (1998), 357–381. (1998) Zbl0913.46028MR1614590
- Cianchi A., A fully anisotropic Sobolev inequality, Preprint no. 15, 1998, Dip. Mat. ”U. Dini”, Univ. di Firenze. (1998) MR1639390
- Cianchi A., Fusco N., Gradient regularity for minimizers under general growth conditions, J. reine angew. Math. 227 (1998), 166–186. (1998) MR1670258
- Cianchi A., Stroffolini B., An extension of Hedberg’s convolution inequality and applications, To appear in J. Math. Anal. Appl. Zbl0914.42014MR1652919
- Donaldson T. K., Nonlinear elliptic boundary value problems in Orlicz-Sobolev spaces, J. Differential Equations 10 (1971), 507–528. (1971) Zbl0218.35028MR0298472
- Donaldson T. K., Trudinger N. S., Orlicz-Sobolev spaces and imbedding theorems, J. Funct. Anal. 8 (1971), 52–75. (1971) Zbl0216.15702MR0301500
- Edmunds D. E., Gurka P., Opic B., Double exponential integrability of convolution operators in generalized Lorentz-Zygmund spaces, Indiana Univ. Math. J. 44 (1995), 19–44. (1995) Zbl0826.47021MR1336431
- Evans W. D., Opic B., Pick L., Interpolation of operators on scales of generalized Lorentz-Zygmund spaces, Math. Nachr. 182 (1996), 127–181. (1996) Zbl0865.46016MR1419893
- Fusco N., Lions P. L., Sbordone C., Some remarks on Sobolev imbeddings in borderline cases, Proc. Amer. Math. Soc. 124 (1996), 561–565. (1996) MR1301025
- Fusco N., Sbordone C., Higher integrability of the gradient of minimizers of functionals with nonstandard growth conditions, Comm. Pure Appl. Math. 43 (1990), 673–683. (1990) Zbl0727.49021MR1057235
- Gehring F. W., The -integrability of the partial derivatives of a quasi conformal mapping, Acta Math. 130 (1973), 265–277. (1973) Zbl0258.30022MR0402038
- Giaquinta M., Giusti E., Quasi-minima, Ann. Inst. H. Poincaré, Anal. Non Linéaire 1 (1984), 79–107. (1984) Zbl0541.49008MR0778969
- Gossez J.-P., Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients, Trans. Amer. Math. Soc. 190 (1974), 163–205. (190 ) MR0342854
- Gossez J.-P., Orlicz-Sobolev spaces and nonlinear elliptic boundary value problems, In: Nonlinear Analysis, Function Spaces and Applications, Vol. 1. S. Fučík and A. Kufner (eds.), Teubner, Leipzig 1979, 59–94. (1979) MR0578910
- Gossez J.-P., A strong nonlinear elliptic problem in Orlicz-Sobolev spaces, Proc. Sympos. Pure Math. 45 (1986), 455–462. (1986) MR0843579
- Gossez J.-P., Mustonen V., Variational inequalities in Orlicz-Sobolev spaces, Nonlinear Anal. 11 (1987), 379–392. (1987) Zbl0643.49006MR0881725
- Greco L., Iwaniec T., Sbordone C., Variational integrals of nearly linear growth, Differential Integral Equations 10 (1997), 687–716. (1997) Zbl0889.35026MR1741768
- Gustavsson J., Peetre J., Interpolation of Orlicz spaces, Studia Math. 60 (1977), 33–59. (1977) Zbl0353.46019MR0438102
- Hempel J. A., Morris G. R., Trudinger N. S., On the sharpness of a limiting case of the Sobolev imbedding theorem, Bull. Austral. Math. Soc. 3 (1970), 369–373. (1970) Zbl0205.12801MR0280998
- Hunt R. A., An extension of the Marcinkiewicz interpolation theorem to Lorentz spaces, Bull. Amer. Math. Soc. 70 (1964), 803–807. (1964) Zbl0145.38203MR0169037
- skii M. A. Krasnosel,’ Rutickii, Ya. B., Convex functions and Orlicz spaces, P. Noordhoff, Groningen 1961. (1961) MR0126722
- Kraynek W. T., Interpolation of sublinear operators in generalized Orlicz and Hardy-Orlicz spaces, Studia Math. 43 (1972), 93–123. (1972) MR0312245
- Kufner A., Weighted Sobolev spaces, Teubner, Leipzig 1980. (1980) Zbl0455.46034MR0664599
- Kufner A., John O., Fučík S., Function Spaces, Noordhoff Int. Publ., Leyden 1977. (1977) MR0482102
- Ladyzhenskaya O. A., tseva N. N. Ural,’, Linear and quasilinear elliptic equations, Academic Press, New York 1968. (1968) MR0244627
- Landes R., Mustonen V., Pseudo monotone mappings in Sobolev-Orlicz spaces and nonlinear boundary value problems on unbounded domains, J. Math. Anal. Appl. 88 (1982), 25–36. (1982) Zbl0492.35015MR0661399
- Lieberman G. M., The natural generalization of the natural conditions of Ladyzhenskaya and Ural’tseva for elliptic equations, Comm. Partial Differential Equations 16 (1991), 311–361. (1991) Zbl0742.35028MR1104103
- Maligranda L., Orlicz spaces and interpolation, Seminários de Matemática, Univ. Estadual de Campinas 1989. (1989) Zbl0874.46022MR2264389
- Marcellini P., Regularity for elliptic equations with general growth conditions, J. Differential Equations 105 (1993), 296–333. (1993) Zbl0812.35042MR1240398
- Marcinkiewicz J., Sur l’interpolation d’operateurs, C. R. Acad. Sci. Paris (1939), 1272–1273. (1939)
- Mascolo E., Papi G., Local boundedness of minimizers of integrals of the calculus of variations, Ann. Mat. Pura Appl. 167 (1994), 323–339. (1994) Zbl0819.49023MR1313560
- Mascolo E., Papi G., Harnack inequality for minimizers of integral functionals with general growth conditions, Nonlinear Differential Equations Appl. 3 (1996), 232–244. (1996) Zbl0855.49027MR1385885
- ya V. G. Maz,’, Sobolev spaces, Springer-Verlag, Berlin 1985. (1985) MR0817985
- Mustonen V., Tienari M., An eigenvalue problem for generalized Laplacian in Orlicz-Sobolev spaces, To appear in Proc. Royal Soc. Edinburgh A. Zbl0926.46030MR1669197
- Neil R. O,’, Fractional integration in Orlicz spaces, Trans. Amer. Math. Soc. 115 (1965), 300–328. (1965) MR0194881
- Opic B., Kufner A., Hardy-type inequalities, Longman Scientific & Technical, Harlow 1990. (1990) Zbl0698.26007MR1069756
- Peetre J., A new approach in interpolation spaces, Studia Math. 34 (1970), 23–42. (1970) Zbl0188.43602MR0264390
- Pokhozhaev S. I., On the imbedding Sobolev theorem for , (Russian.) Doklady conference, Section Math., Moscow Power Institute (1965), 158–170. (1965)
- nik E. I. Pustyl,’, On optimal interpolation and some interpolation properties of Orlicz spaces, Soviet Math. Dokl. 27 (1983). (1983) MR0698510
- Rao M. M., Interpolation, ergodicity and martingales, J. Math. Mech. 16 (1966), 543–567. (1966) Zbl0166.11704MR0207960
- Rao M. M., Ren Z. D., Theory of Orlicz spaces, Marcel Dekker Inc., New York 1991. (1991) Zbl0724.46032MR1113700
- Riordan W. J., On the interpolation of operators, PhD Dissertation, Univ. Chicago 1956 (see also Notices Amer. Math. Soc. 5 (1958), 590). (1956)
- Sawyer E. T., Boundedness of classical operators on classical Lorentz spaces, Studia Math. 96 (1990), 145–158. (1990) Zbl0705.42014MR1052631
- Sbordone C., On some integral inequalities and their applications to the Calculus of Variations, Boll. Un. Mat. Ital., Analisi Funzionale e Applicazioni, Ser VI 5 (1986), 73–94. (1986) Zbl0678.49008MR0897186
- Stampacchia G., On some regular multiple integral problems in the calculus of variations, Comm. Pure Appl. Math. 16 (1963), 383–421. (1963) Zbl0138.36903MR0155209
- Stredulinsky E. W., Higher integrability from reverse Hölder inequalities, Indiana Univ. Math. J. 29 (1980), 407–413. (1980) Zbl0442.35064MR0570689
- Strichartz R. S., A note on Trudinger’s extension of Sobolev’s inequalities, Indiana Univ. Math. J. 21 (1972), 841–842. (1972) Zbl0241.46028MR0293389
- Talenti G., Best constant in Sobolev inequality, Ann. Mat. Pura Appl. 110 (1976), 353–372. (1976) Zbl0353.46018MR0463908
- Talenti G., Elliptic equations and rearrangements, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3 (1976), 697–718. (1976) Zbl0341.35031MR0601601
- Talenti G., An embedding theorem, Essays of Math. Analysis in honour of E. De Giorgi, Birkhäuser, Boston 1989. (1989) Zbl0702.46020MR1034035
- Talenti G., Boundedness of minimizers, Hokkaido Math. J. XIX (1990), 259–279. (1990) Zbl0723.58015MR1059170
- Talenti G., Inequalities in rearrangement invariant function spaces, In: Nonlinar Analysis, Function Spaces and Applications, vol. 5. M. Krbec, A. Kufner, B. Opic and J. Rákosník (eds.), Prometheus Publishing House, Prague 1994, 177–230. (1994) Zbl0872.46020MR1322313
- Torchinsky A., Interpolation of operators and Orlicz classes, Studia Math. 59 (1976), 177–207. (1976) MR0438105
- Torchinsky A., Real variable methods in harmonic analysis, Academic Press, San Diego 1986. (1986) Zbl0621.42001MR0869816
- Trudinger N. S., On imbeddings into Orlicz spaces and some applications, J. Math. Mech. 17 (1967), 473–483. (1967) Zbl0163.36402MR0216286
- Yudovich V. I., Certain estimates connected with integral operators and solutions of elliptic equations, Dokl. Akad. Nauk SSSR 138 (1961), 805–808. (1961) MR0140822
- Ziemer W. P., Weakly differentiable functions, Springer-Verlag, New York 1989. (1989) Zbl0692.46022MR1014685
- Zygmund A., On a theorem of Marcinkiewicz concerning interpolation of operations, J. Math. Pures Appl. 35 (1956), 223–248. (1956) Zbl0070.33701MR0080887
Citations in EuDML Documents
top- Lars Diening, Bianca Stroffolini, Anna Verde, Lipschitz regularity for some asymptotically convex problems
- Lars Diening, Bianca Stroffolini, Anna Verde, Lipschitz regularity for some asymptotically convex problems
- Agnieszka Kałamajska, Katarzyna Pietruska-Pałuba, New Orlicz variants of Hardy type inequalities with power, power-logarithmic, and power-exponential weights
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.