Characterization of the interior regularity for parabolic systems with discontinuous coefficients

Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni

Volumn 16, Issue 2, 2005, Pages 127-132

  Palagachev, Dian K ^a   Softova, Lubomira G ^b  

^a POLITECNICO DI BARI   (Italy)

^b INSTITUTE OF MATHEMATICS AND INFORMATICS   (Bulgaria)

Author keywords

A priori estimates; H lder regularity; Morrey spaces; Parabolic systems; VMO

Indexed keywords

EID: 33646889993     PISSN: 11206330     EISSN: 17200768     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. S. Agmon - A. Douglis -L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differentialequationssatisfyinggeneralboundary conditions. I. Comm. Pure Appi. Math., vol. 12,1959,623-727.
2. S. Agmon - A. Douglis -L.Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II. Comm. Pure Appi. Math., vol. 17, 1964, 35-92.
3. S. Campanato, Proprietàdi' Hölderianità di alcune classi di funzioni. Ann. Scuola Norm. Sup. Pisa, vol. 17, 1963, 175-188.
4. F. Chiarenza -M.Franciosi -M.Frasca, LP -Estimates for linear elliptic systems with discontinuous coefficients. Rend. Mat. Acc. Lincei, s. 9, vol. 5, 1994, 27-32.
5. G. Da Prato, Spazi LP-θ(Ω, Σ) e loro proprietà. Ann. Mat. Pura Appl., vol. 69, 1965, 383-392.
6. A. Douglis -L.Nirenberg, Interior estimates for elliptic systems of partial differential equations. Comm. Pure Appl. Math., vol. 8, 1955, 503-538.
7. S.D. Ejdel'man, Parabolic Equations. In: Yu.V. Egorov - M.A. Shubin (eds.), Partial Differential Equations VI: Elliptic and Parabolic Operators. Encycl. Math. Sci., vol. 63, Springer-Verlag, Berlin 1994, 203-316.
8. E.B. Fabes -N. Rivière, Singular integrals with mixed homogeneity. Studia Math., vol. 27, 1966, 19-38.
9. A. Friedman, Partial Differential Equations of Parabolic Type. Prentice-Hall, Englewood Cliffs, N.J., 1964.
10. F. John -L. Nirenberg, On functions of bounded mean oscillation. Comm. Pure Appl. Math., vol. 14, 1961, 415-426.
11. M. Kronz, Some function spaces on spaces of homogeneous type. Manuscr. Math., vol. 106,2001,219-248.
12. A. Maugeri - D.K. Palagachev - L.G. Softova, Elliptic and Parabolic Equations with Discontinuous Coefficients. Wiley-VCH, Berlin 2000.
13. D.K. Palagachev - L.G. Softova, Singular integral operators, Morrey spaces and fine regularity of solutions to PDE's. Potential Anal., vol. 20, 2004, 237-263. (Pubitemid 39045911)
14. D. Sarason, Functions of vanishing mean oscillation. Trans. Amer. Math. Soc., vol. 207, 1975, 391-405.
15. V.A. Solonnikov, On the boundary value problems for linear parabolic systems of differential equations of general form. Proc. Steklov Inst. Math., vol. 83, 1965 (in Russian);
16. English translation: O.A. Ladyzhenskaya (ed.), Boundary Value Problems of Mathematical Physics III. Amer. Math. Soc., Providence, R.I., 1967.