Title:
|
A maximum principle for linear elliptic systems with discontinuous coefficients (English) |
Author:
|
Leonardi, S. |
Language:
|
English |
Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
ISSN:
|
0010-2628 (print) |
ISSN:
|
1213-7243 (online) |
Volume:
|
45 |
Issue:
|
3 |
Year:
|
2004 |
Pages:
|
457-474 |
. |
Category:
|
math |
. |
Summary:
|
We prove a maximum principle for linear second order elliptic systems in divergence form with discontinuous coefficients under a suitable condition on the dispersion of the eigenvalues of the coefficients matrix. (English) |
Keyword:
|
maximum principle |
Keyword:
|
elliptic systems |
MSC:
|
35B50 |
MSC:
|
35B65 |
MSC:
|
35J55 |
MSC:
|
35R05 |
idZBL:
|
Zbl 1098.35044 |
idMR:
|
MR2103140 |
. |
Date available:
|
2009-05-05T16:46:30Z |
Last updated:
|
2012-04-30 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119473 |
. |
Reference:
|
[1] Campanato S.: Equazioni ellittiche del II$^o$ ordine e spazi ${\Cal L}^{2,\lambda}$.Ann. Mat. Pura Appl. (4) 69 (1965), 321-381. MR 0192168 |
Reference:
|
[2] Campanato S.: Maggiorazioni interpolatorie negli spazi $H^{m,p}_{\lambda}(Ømega)$.Ann. Mat. Pura Appl. (4) 75 (1967), 261-276. MR 0216284 |
Reference:
|
[3] Campanato S.: Sistemi Ellittici in forma divergenza. Regolarità all' interno.Quaderni Scuola Normale Superiore Pisa, Pisa, 1980. Zbl 0453.35026, MR 0668196 |
Reference:
|
[4] Campanato S.: A maximum principle for non-linear elliptic systems: boundary fundamental estimates.Adv. in Math. 66 (1987), 291-317. MR 0915857 |
Reference:
|
[5] Cannarsa P.: On a maximum principle for elliptic systems with constant coefficients.Rend. Sem. Univ. Padova 64 (1981). Zbl 0473.35016, MR 0636627 |
Reference:
|
[6] de Giorgi E.: Sulla differenziabilitá e l'analiticità delle estremali degli integrali multipli regolari.Memorie dell'Accademia delle Scienze di Torino, Serie 3, 3(I) (1957). Zbl 0084.31901 |
Reference:
|
[7] de Giorgi E.: Un esempio di estremali discontinue per un problema variazionale di tipo ellittico.Boll. Un. Mat. Ital. (4) 1 (1968), 135-137. MR 0227827 |
Reference:
|
[8] Giaquinta M.: Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems.Annals of Math. Studies, Princeton University Press, Princeton, 1983. Zbl 0516.49003, MR 0717034 |
Reference:
|
[9] Gilbarg D., Trudinger N.S.: Elliptic Partial Differential Equations of Second Order.second edition., Springer, 1983. Zbl 1042.35002, MR 0737190 |
Reference:
|
[10] Kalita E.: On the Hölder continuity of solutions of nonlinear parabolic systems.Comment. Math. Univ. Carolinae 35.4 (1994), 675-680. Zbl 0814.35011, MR 1321237 |
Reference:
|
[11] Koshelev A.I.: Regularity Problem for Quasilinear Elliptic and Parabolic Systems.Springer, 1995. Zbl 0847.35023, MR 1442954 |
Reference:
|
[12] Kottas J.: Interior regularity for the quasilinear elliptic systems with nonsmooth coefficients.Comment. Math. Univ. Carolinae 28.1 (1987), 95-102. MR 0889771 |
Reference:
|
[13] Kottas J.: Regularita slabých řešení eliptických úloh.Thesis of Dissertation, Charles University, Prague, 1990. |
Reference:
|
[14] Kufner A., John O., Fučík S.: Function Spaces.Noordhoff Int. Pub. Leyden, Academia Prague, 1977. MR 0482102 |
Reference:
|
[15] Leonardi S.: On constants of some regularity theorems. De Giorgi's type counterexample.Math. Nachr. 192 (1998). Zbl 0909.35030, MR 1626336 |
Reference:
|
[16] Leonardi S.: Remarks on the regularity of solutions of elliptic systems.Kluwer Academic/ Plenum Publishers, New York, 1999. Zbl 0952.35034, MR 1727457 |
Reference:
|
[17] Maz'ya V.G.: Examples of nonregular solutions of quasilinear elliptic equations with analytic coefficients.Funktsional'nyi Analiz. i Ego Prilosheniya 2 (1968). Zbl 0179.43601, MR 0237946 |
Reference:
|
[18] Meyers N.G.: An $L^p$ estimate for the gradient of solutions of second order elliptic divergence equations.Ann. Scuola Norm. Sup. Pisa, (3) 17 (1963). MR 0159110 |
Reference:
|
[19] Miranda C.: Istituzioni di Analisi Funzionale Lineare.U.M.I. 1978. Zbl 0697.46002 |
Reference:
|
[20] Nečas J.: Les Méthodes Directes en Théorie des Équationes elliptiques.Masson et Cie, Éditeurs, Paris, 1967. MR 0227584 |
Reference:
|
[21] Nečas J.: On the regularity of weak solutions to nonlinear elliptic systems of partial differential equations.Lectures at Scuola Normale Superiore, Pisa, 1979. |
Reference:
|
[22] Nečas J.: Introduction to the Theory of Nonlinear Elliptic Equations.Teubner-Texte Math., Leipzig, 1983 or J. Wiley, Chichester, 1986. MR 0874752 |
Reference:
|
[23] Nečas J., Stará J.: Principio di massimo per sistemi ellittici quasi lineari non diagonali.Boll. Un. Mat. Ital. (4) 6 (1972), 1-10. MR 0315281 |
. |