The Dirichlet problem for elliptic equations in the plane

Paola Cavaliere; Maria Transirico

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 4, page 751-758
  • ISSN: 0010-2628

Abstract

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In this paper an existence and uniqueness theorem for the Dirichlet problem in W 2 , p for second order linear elliptic equations in the plane is proved. The leading coefficients are assumed here to be of class VMO.

How to cite

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Cavaliere, Paola, and Transirico, Maria. "The Dirichlet problem for elliptic equations in the plane." Commentationes Mathematicae Universitatis Carolinae 46.4 (2005): 751-758. <http://eudml.org/doc/249570>.

@article{Cavaliere2005,
abstract = {In this paper an existence and uniqueness theorem for the Dirichlet problem in $W^\{2,p\}$ for second order linear elliptic equations in the plane is proved. The leading coefficients are assumed here to be of class VMO.},
author = {Cavaliere, Paola, Transirico, Maria},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {elliptic equations; VMO-coefficients; elliptic equation; Dirichlet problem; VMO-coeficients},
language = {eng},
number = {4},
pages = {751-758},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The Dirichlet problem for elliptic equations in the plane},
url = {http://eudml.org/doc/249570},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Cavaliere, Paola
AU - Transirico, Maria
TI - The Dirichlet problem for elliptic equations in the plane
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 4
SP - 751
EP - 758
AB - In this paper an existence and uniqueness theorem for the Dirichlet problem in $W^{2,p}$ for second order linear elliptic equations in the plane is proved. The leading coefficients are assumed here to be of class VMO.
LA - eng
KW - elliptic equations; VMO-coefficients; elliptic equation; Dirichlet problem; VMO-coeficients
UR - http://eudml.org/doc/249570
ER -

References

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  1. Astala K., Iwaniec T., Martin G., Pucci's conjecture and the Alexandrov inequality for elliptic PDEs in the plane, to appear. Zbl1147.35021
  2. Caso L., Cavaliere P., Transirico M., Uniqueness results for elliptic equations with VMO-coefficients, Int. J. Pure Appl. Math. 13 (2004), 499-512. (2004) MR2068723
  3. Caso L., Cavaliere P., Transirico M., An existence result for elliptic equations with VMO-coefficients, J. Math. Anal. Appl., to appear. Zbl1152.35025MR2270071
  4. Chiarenza F., Frasca M., Longo P., Interior W 2 , p estimates for non divergence elliptic equations with discontinuous coefficients, Ricerche Mat. 40 (1991), 149-168. (1991) MR1191890
  5. Chiarenza F., Frasca M., Longo P., W 2 , p -solvability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients, Trans. Amer. Math. Soc. 336 (1993), 841-853. (1993) MR1088476
  6. Glushak A.V., Transirico M., Troisi M., Teoremi di immersione ed equazioni ellittiche in aperti non limitati, Rend. Mat. Appl. (7) 9 (1989), 113-130. (1989) MR1044521
  7. Maugeri A., Palagachev D.K., Softova L.G., Elliptic and Parabolic Equations with Discontinuous Coefficients, Wiley, Berlin, 2000. Zbl0958.35002MR2260015
  8. Pucci C., Equazioni ellittiche con soluzioni in W 2 , p , p < 2 , Atti del Convegno sulle Equazioni alle Derivate Parziali (Bologna, 1967), pp.145-148; MR42-6413. MR0271530
  9. Talenti G., Equazioni lineari ellittiche in due variabili, Matematiche (Catania) 21 (1966), 339-376. (1966) Zbl0149.07402MR0204845
  10. Transirico M., Troisi M., Vitolo A., BMO spaces on domains of n , Ricerche Mat. 45 (1996), 355-378. (1996) MR1776414
  11. Vitanza C., W 2 , p -regularity for a class of elliptic second order equations with discontinuous coefficients, Matematiche (Catania) 47 (1992), 177-186. (1992) MR1229461
  12. Vitanza C., A new contribution to the W 2 , p -regularity for a class of elliptic second order equations with discontinuous coefficients, Matematiche (Catania) 48 (1993), 287-296. (1993) MR1320669

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