| Title:
|
A generalized maximum principle for boundary value problems for degenerate parabolic operators with discontinuous coefficients (English) |
| Author:
|
Bonafede, Salvatore |
| Author:
|
Nicolosi, Francesco |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
125 |
| Issue:
|
1 |
| Year:
|
2000 |
| Pages:
|
39-54 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove a generalized maximum principle for subsolutions of boundary value problems, with mixed type unilateral conditions, associated to a degenerate parabolic second-order operator in divergence form. (English) |
| Keyword:
|
weak subsolution |
| Keyword:
|
generalized maximum principle |
| Keyword:
|
comparison theorem |
| Keyword:
|
degenerate equation |
| MSC:
|
35B50 |
| MSC:
|
35K10 |
| MSC:
|
35K65 |
| MSC:
|
35K85 |
| idZBL:
|
Zbl 0963.35033 |
| idMR:
|
MR1752078 |
| DOI:
|
10.21136/MB.2000.126266 |
| . |
| Date available:
|
2009-09-24T21:40:03Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126266 |
| . |
| Reference:
|
[1] Adams R. A.: Sobolev Spaces.Academic Press, New York, 1975. Zbl 0314.46030, MR 0450957 |
| Reference:
|
[2] Baiocchi C.: Soluzioni deboli dei problemi ai limiti per le equazioni paraboliche del tipo del calore.Ist. Lombardo Accad. Sci. Lett. Rend. Sez. A 103 (1969), 704-726. MR 0262696 |
| Reference:
|
[3] Bonafede S.: On maximum principle for weak subsolutions of degenerate parabolic linear equations.Comment. Math. Univ. Carolin. 35 (1994), 417-430. Zbl 0808.35065, MR 1307270 |
| Reference:
|
[4] Bonafede S.: A generalized maximum principle for weak subsolutions of degenerate parabolic equations.Rend. Circ. Mat. Palermo (2) 41 (1992), 81-95. MR 1175590 |
| Reference:
|
[5] Drábek P., Nicolosi F.: Existence of bounded solutions for some degenerated quasilinear elliptic equations.Ann. Mat. Pura Appl. (4) 165 (1993), 217-238. MR 1271420 |
| Reference:
|
[6] Eklund N. A.: Generalized super-solution of parabolic operators.Trans. Amer. Math. Soc. 220 (1976), 235-242. MR 0473522, 10.1090/S0002-9947-1976-0473522-6 |
| Reference:
|
[7] Guglielmino F., Nicolosi F.: W-solutions of boundary value problems for degenerate elliptic operators.Ricerche Mat. Suppl. 36 (1987), 59-72. MR 0956018 |
| Reference:
|
[8] Guglielmino F., Nicolosi F.: Existence theorems for boundary value problems associated with quasilinear elliptic equations.Ricerche Mat. 37 (1988), 157-176. MR 1021963 |
| Reference:
|
[9] Guglielmino F., Nicolosi F.: Existence results for boundary value problems for a class of quasilinear parabolic equations.Actual problems in analysis and mathematical physics, Proceeding of the international symposium in Taormina, Italy, 1992. Univ. di Roma, Roma, 1993, pp. 95-117. |
| Reference:
|
[10] Ladyzhenskaja O. A., Solonnikov V. A., Ural'tseva N. N.: Linear and Quasi-Linear Equations of Parabolic Type.Translation of mathematical monographs, vol. 23, A. M. S. Providence, 1968. |
| Reference:
|
[11] Murthy M. K. V., Stampacchia G.: Boundary value problems for some degenerate-elliptic operators.Ann. Mat. Pura Appl. (4) 80 (1968), 1-122. Zbl 0185.19201, MR 0249828, 10.1007/BF02413623 |
| Reference:
|
[12] Nicolosi F.: Sottosoluzioni deboli delle equazioni paraboliche lineari del secondo ordine superiormente limitate.Matematiche 28 (1973), 361-378. MR 0364867 |
| Reference:
|
[13] Nicolosi F.: Soluzioni dei problemi al contorno per operatori parabolici che possono degenerare.Ann. Mat. Pura Appl., IV. Ser. 125 (1980), 135-155. MR 1553443 |
| Reference:
|
[14] Platone Garroni M. G.: A generalized maximum principle for boundary value problems for elliptic operators with discontinuous coefficients.Boll. U.M.I. (4) 9 (1974), 1-9. Zbl 0294.35025, MR 0372415 |
| Reference:
|
[15] Protter M. H., Weinberger H. F.: Regular points for elliptic equations with discontinuous coefficients.Ann. Scuola Sup. Pisa 17 (1963), 45-79. MR 0161019 |
| Reference:
|
[16] Stampacchia G.: Le probleme de Dirichiet pour les equations elliptiques du second ordre a coefficients discontinus.Annal. Inst. Fourier 15 (1965), 187-257. MR 0192177 |
| Reference:
|
[17] Troianello G. M.: On weak subsolutions for parabolic second-order operators.Comm. Partial Differential Equations 3, 933-948. MR 0507123, 10.1080/03605307808820081 |
| . |
