| Title:
|
On maximum principle for weak subsolutions of degenerate parabolic linear equations (English) |
| Author:
|
Bonafede, Salvatore |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
3 |
| Year:
|
1994 |
| Pages:
|
417-430 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Sufficient conditions are obtained so that a weak subsolution of $(0.1)$, bounded from above on the parabolic boundary of the cylinder $Q$, turns out to be bounded from above in $Q$. (English) |
| Keyword:
|
maximum principle |
| Keyword:
|
weak subsolution |
| Keyword:
|
degenerate equation |
| MSC:
|
35B50 |
| MSC:
|
35K10 |
| MSC:
|
35K65 |
| idZBL:
|
Zbl 0808.35065 |
| idMR:
|
MR1307270 |
| . |
| Date available:
|
2009-01-08T18:12:16Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118683 |
| . |
| Reference:
|
[1] Bonafede S.: Sottosoluzioni deboli delle equazioni paraboliche lineari del secondo ordine degeneri.Rendiconti del circolo Matematico di Palermo, Serie II, Tomo XXXIX (1990), 132-152. |
| Reference:
|
[2] Eklund N.A.: Generalized super-solution of parabolic equations.Transaction of the American Mathematical Society 220 (1976), 235-242. MR 0473522 |
| Reference:
|
[3] Gagliardo E.: Proprieta' di alcune classi di funzioni in piu' variabili.Ricerche di Matematica 7 (1958), 102-137. Zbl 0089.09401, MR 0102740 |
| Reference:
|
[4] Ivanov A.V.: Properties of solutions of linear and quasilinear second-order equations with measurable coefficients which are neither strictly nor non uniformly parabolic.Zap. Nauch. Sem. Leningrad Otdel Mat. Inst. Steklov (LOMI) 69 (1977), 45-65 Transl. in Journal of Soviet Math., 10 (1978), pp. 29-43. MR 0603301 |
| Reference:
|
[5] Ladyzhenskaya O.A., Ural'tseva N.N.: Linear and quasilinear elliptic equations.Academic Press, New York, 1968. Zbl 0177.37404, MR 0244627 |
| Reference:
|
[6] Nicolosi F.: Sottosoluzioni deboli delle equazioni paraboliche lineari del secondo ordine superiormente limitate.Le Matematiche 28 (1973), 361-378. MR 0364867 |
| Reference:
|
[7] Nicolosi F.: Soluzioni deboli dei problemi al contorno per operatori parabolici che possono degenerare.Annali di Matematica (4) 125 (1980), 135-155. Zbl 0452.35065, MR 1553443 |
| Reference:
|
[8] Stampacchia G.: Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus.Annal. Inst. Fourier 15 (1965), 189-257. Zbl 0151.15401, MR 0192177 |
| Reference:
|
[9] Troianello G.M.: On weak subsolutions for parabolic second-order operators.Comm. in Partial Diff. Equat. 3 (10), 933-948. MR 0507123 |
| . |
