| Title:
|
The Dirichlet problem for elliptic equations in the plane (English) |
| Author:
|
Cavaliere, Paola |
| Author:
|
Transirico, Maria |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
751-758 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 {\it VMO\/}. (English) |
| Keyword:
|
elliptic equations |
| Keyword:
|
{\it VMO\/}-coefficients |
| MSC:
|
30G20 |
| MSC:
|
35J25 |
| MSC:
|
35R05 |
| idZBL:
|
Zbl 1121.35040 |
| idMR:
|
MR2259505 |
| . |
| Date available:
|
2009-05-05T16:54:53Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119565 |
| . |
| Reference:
|
[1] Astala K., Iwaniec T., Martin G.: Pucci's conjecture and the Alexandrov inequality for elliptic PDEs in the plane.to appear. Zbl 1147.35021 |
| Reference:
|
[2] Caso L., Cavaliere P., Transirico M.: Uniqueness results for elliptic equations with VMO-coefficients.Int. J. Pure Appl. Math. 13 (2004), 499-512. MR 2068723 |
| Reference:
|
[3] Caso L., Cavaliere P., Transirico M.: An existence result for elliptic equations with VMO-coefficients.J. Math. Anal. Appl., to appear. Zbl 1152.35025, MR 2270071 |
| Reference:
|
[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. MR 1191890 |
| Reference:
|
[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. MR 1088476 |
| Reference:
|
[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. MR 1044521 |
| Reference:
|
[7] Maugeri A., Palagachev D.K., Softova L.G.: Elliptic and Parabolic Equations with Discontinuous Coefficients.Wiley, Berlin, 2000. Zbl 0958.35002, MR 2260015 |
| Reference:
|
[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. MR 0271530 |
| Reference:
|
[9] Talenti G.: Equazioni lineari ellittiche in due variabili.Matematiche (Catania) 21 (1966), 339-376. Zbl 0149.07402, MR 0204845 |
| Reference:
|
[10] Transirico M., Troisi M., Vitolo A.: BMO spaces on domains of $\Bbb R^n$.Ricerche Mat. 45 (1996), 355-378. MR 1776414 |
| Reference:
|
[11] Vitanza C.: $W^{2,p}$-regularity for a class of elliptic second order equations with discontinuous coefficients.Matematiche (Catania) 47 (1992), 177-186. MR 1229461 |
| Reference:
|
[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. MR 1320669 |
| . |
