Functions with derivatives in spaces of Morrey type and elliptic equations in unbounded domains

Anna Canale; Patrizia Di Gironimo; Antonio Vitolo

Studia Mathematica (1998)

  • Volume: 128, Issue: 3, page 199-218
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Canale, Anna, Di Gironimo, Patrizia, and Vitolo, Antonio. "Functions with derivatives in spaces of Morrey type and elliptic equations in unbounded domains." Studia Mathematica 128.3 (1998): 199-218. <http://eudml.org/doc/216483>.

@article{Canale1998,
abstract = {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.},
author = {Canale, Anna, Di Gironimo, Patrizia, Vitolo, Antonio},
journal = {Studia Mathematica},
keywords = {unique solution; Morrey space; extension operator; Fredholm operator},
language = {eng},
number = {3},
pages = {199-218},
title = {Functions with derivatives in spaces of Morrey type and elliptic equations in unbounded domains},
url = {http://eudml.org/doc/216483},
volume = {128},
year = {1998},
}

TY - JOUR
AU - Canale, Anna
AU - Di Gironimo, Patrizia
AU - Vitolo, Antonio
TI - Functions with derivatives in spaces of Morrey type and elliptic equations in unbounded domains
JO - Studia Mathematica
PY - 1998
VL - 128
IS - 3
SP - 199
EP - 218
AB - 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.
LA - eng
KW - unique solution; Morrey space; extension operator; Fredholm operator
UR - http://eudml.org/doc/216483
ER -

References

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  1. [AD] R. A. Adams, Sobolev Spaces, Academic Press, 1971, 239-258. 
  2. [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. Zbl0833.35033
  3. [CLM₂] A. Canale, M. Longobardi and G. Manzo, Existence and uniqueness results for second order elliptic equations in unbounded domains, ibid., 171-187. Zbl0847.35039
  4. [CF] F. Chiarenza and M. Franciosi, A generalization of a theorem by C. Miranda, Ann. Mat. Pura Appl. (4) 161 (1992), 285-297. 
  5. [CFR] F. Chiarenza and M. Frasca, A remark on a paper by C. Fefferman, Proc. Amer. Math. Soc. 108 (1990), 407-409. 
  6. [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. Zbl0289.35071
  7. [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. Zbl0486.35078
  8. [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. 
  9. [KJF] A. Kufner, O. John and S. Fučik, Function Spaces, Noordhoff, Leyden, 1977. 
  10. [M] C. Miranda, Sulle equazioni ellittiche di tipo non variazionale a coefficienti discontinui, Ann. Mat. Pura Appl. (4) 63 (1963), 353-386. Zbl0156.34001
  11. [TT₁] M. Transirico and M. Troisi, Equazioni ellittiche del secondo ordine di tipo non variazionale in aperti non limitati, ibid. 152 (1988), 209-226. 
  12. [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 . 
  13. [TT₃] M. Transirico and M. Troisi, Equazioni ellittiche del secondo ordine tipo Cordes in aperti non limitati di ℝ n , Boll. Un. Mat. Ital. B (7) 3 (1989), 169-184. 
  14. [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. 
  15. [V] A. Vitolo, Functions with derivatives in spaces of Morrey type, Rend. Acad. Naz. Sci. XL Mem. Mat. 21 (1997), to appear. 

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