Functions with derivatives in spaces of Morrey type and elliptic equations in unbounded domains
Canale, Anna ; Di Gironimo, Patrizia ; Vitolo, Antonio
Studia Mathematica, Tome 129 (1998), p. 199-218 / Harvested from The Polish Digital Mathematics Library
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We introduce a sort of "local" Morrey spaces and show an existence and uniqueness theorem for the Dirichlet problem in unbounded domains for linear second order elliptic partial differential equations with principal coefficients "close" to functions having derivatives in such spaces.

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:216483 
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     title = {Functions with derivatives in spaces of Morrey type and elliptic equations in unbounded domains},
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     volume = {129},
     year = {1998},
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Canale, Anna; Di Gironimo, Patrizia; Vitolo, Antonio. Functions with derivatives in spaces of Morrey type and elliptic equations in unbounded domains. Studia Mathematica, Tome 129 (1998) pp. 199-218. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv128i3p199bwm/

[00000] [AD] R. A. Adams, Sobolev Spaces, Academic Press, 1971, 239-258.

[00001] [CLM₁] A. Canale, M. Longobardi and G. Manzo, Second order elliptic equations with discontinuous coefficients in unbounded domains, Rend. Accad. Naz. Sci. XL Mem. Mat. 18 (1994), 41-56. | Zbl 0833.35033

[00002] [CLM₂] A. Canale, M. Longobardi and G. Manzo, Existence and uniqueness results for second order elliptic equations in unbounded domains, ibid., 171-187. | Zbl 0847.35039

[00003] [CF] F. Chiarenza and M. Franciosi, A generalization of a theorem by C. Miranda, Ann. Mat. Pura Appl. (4) 161 (1992), 285-297.

[00004] [CFR] F. Chiarenza and M. Frasca, A remark on a paper by C. Fefferman, Proc. Amer. Math. Soc. 108 (1990), 407-409.

[00005] [C₁] M. Chicco, Principio di massimo per le soluzioni di equazioni ellittiche del secondo ordine di tipo Cordes, Ann. Mat. Pura Appl. (4) 100 (1974), 239-258. | Zbl 0289.35071

[00006] [C₂] M. Chicco, Osservazioni sulla risolvibilità del problema di Dirichlet per una classe di equazioni ellittiche a coefficienti discontinui, Rend. Sem. Mat. Univ. Padova 66 (1982), 137-141. | Zbl 0486.35078

[00007] [GTT] A. V. Glushak, M. Transirico and M. Troisi, Teoremi di immersione ed equazioni ellittiche in aperti non limitati, Rend. Mat. (7) 9 (1989), 113-130.

[00008] [KJF] A. Kufner, O. John and S. Fučik, Function Spaces, Noordhoff, Leyden, 1977.

[00009] [M] C. Miranda, Sulle equazioni ellittiche di tipo non variazionale a coefficienti discontinui, Ann. Mat. Pura Appl. (4) 63 (1963), 353-386. | Zbl 0156.34001

[00010] [TT₁] M. Transirico and M. Troisi, Equazioni ellittiche del secondo ordine di tipo non variazionale in aperti non limitati, ibid. 152 (1988), 209-226.

[00011] [TT₂] M. Transirico and M. Troisi, Su una classe di equazioni ellittiche del secondo ordine in aperti non limitati, Rend. Mat. (7) 8 (1988), 1-17 .

[00012] [TT₃] M. Transirico and M. Troisi, Equazioni ellittiche del secondo ordine tipo Cordes in aperti non limitati di ℝn, Boll. Un. Mat. Ital. B (7) 3 (1989), 169-184.

[00013] [TTV] M. Transirico, M. Troisi and A. Vitolo, Spaces of Morrey type and elliptic equations in divergence form on unbounded domains, ibid. 9 (1995), 153-174.

[00014] [V] A. Vitolo, Functions with derivatives in spaces of Morrey type, Rend. Acad. Naz. Sci. XL Mem. Mat. 21 (1997), to appear.