Previous |  Up |  Next

Article

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
.

Files

Files Size Format View
CommentatMathUnivCarolRetro_45-2004-3_7.pdf 259.3Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo