Quasilinear parabolic operators with discontinuous ingredients

Nonlinear Analysis, Theory, Methods and Applications

Volumn 52, Issue 4, 2003, Pages 1079-1093

  Softova, Lubomira G ^a  

^a INSTITUTE OF MATHEMATICS AND INFORMATICS   (Bulgaria)

Author keywords

A priori estimates; Leray Schauder fixed point theorem; Oblique derivative problem; Parabolic operators; Strong solvability; VMO

Indexed keywords

BOUNDARY VALUE PROBLEMS; FUNCTIONS; SET THEORY;

QUASILINEAR PARABOLIC OPERATORS;

MATHEMATICAL OPERATORS;

EID: 0037290407     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(02)00128-1     Document Type: Article

References (29)

1. Acquistapace P. On BMO regularity for linear elliptic systems. Ann. Mat. Pura Appl. 161:1992;231-270.
2. Amann H., Crandall M. On some existence theorems for semi-linear elliptic equations. Indiana Univ. Math. J. 27:1978;779-790.
3. 1,2 solvability for the Cauchy-Dirichlet problem for parabolic equations with VMO coefficients Comm. Partial Differential Equations. 18:1993;1735-1763.
4. p regularity for systems of PDE's with coefficients in VMO, in: Nonlinear Analysis, Function Spaces and Applications, Vol. 5, Prague, 1994, http://www.emis.de/proceedings/Praha94/3.html.
5. 2,p estimates for nondivergence elliptic equations with discontinuous coefficients Ricerche Mat. 40:1991;149-168.
6. 2,p solvability of the Dirichlet problem for nondivergence form elliptic equations with VMO coefficients Trans. Amer. Math. Soc. 336:1993;841-853.
7. Di Fazio G., Palagachev D.K. Oblique derivative problem for quasilinear elliptic equations with VMO coefficients. Bull. Austral. Math. Soc. 53:1996;501-513.
8. Fučik S., Kufner A. Nonlinear Differential Equations. 1980;Elsevier Science Publishers, New York.
9. Gilbarg G., Trudinger N.S. Elliptic Partial Differential Equations of Second Order. 2nd Edition:1983;Springer, Berlin.
10. John F., Nirenberg L. On functions of bounded mean oscillation. Comm. Pure Appl. Math. 14:1961;415-426.
11. Jones P.W. Extension theorems for BMO. Indiana Univ. Math. J. 29:1980;41-66.
12. Ladyzhenskaya O.A., Solonnikov V.A., Ural'ceva N.N. Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical Monographs. Vol. 23:1968;American Mathematical Society, Providence, RI.
13. Ladyzhenskaya O.A., Ural'tseva N.N. Linear and Quasilinear Elliptic Equations. 1968;Academic Press, New York, London.
14. Ladyzhenskaya O.A., Ural'tseva N.N. A survey of results on the solubility of boundary-value problems for second-order uniformly elliptic and parabolic quasi-linear equations having unbounded singularities. Russian Math. Surveys. 41(5):1986;1-31.
15. Markowich P. The Stationary Semiconductor Devise Equations. 1986;Springer, Vienna.
16. Maugeri A., Palagachev D.K. Boundary value problem with an oblique derivative for uniformly elliptic operators with discontinuous coefficients. Forum Math. 10:1998;393-405.
17. Maugeri A., Palagachev D.K., Softova L.G. Elliptic and Parabolic Equations with Discontinuous Coefficients. 2000;Wiley, Berlin.
18. Merion R. Continuous Time Finance. 1990;Blackwell, Cambridge.
19. A.I. Nazarov, Hölder estimates for bounded solutions of problems with an oblique derivative for parabolic equations of nondivergence structure, J. Soviet Math. 64 (6) (1993) 1247-1252 (Transl. from Probl. Mat. Anal. (11) (1990) 37-46).
20. A.I. Nazarov, N.N. Ural'tseva, Convex-monotone hulls and estimation of the maximum of a solution of a parabolic equation, J. Soviet Math. 37 (1987) 851-859 (Transl. from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. im. V.A. Steklov AN SSSR 147 (1985) 95-109).
21. A.I. Nazarov, N.N. Ural'tseva, The oblique boundary-value problem for a quasilinear parabolic equation, J. Math. Sci. 77 (3) (1995) 3212-3220 (Transl. from Zap. Nauchn. Semin. POMI 200 (1992) 118-131).
22. Palagachev D.K. Quasilinear elliptic equations with VMO coefficients. Trans. Amer. Math. Soc. 347:1995;2481-2493.
23. Palagachev D.K., Ragusa M.A., Softova L.G. Regular oblique derivative problem in Morrey spaces. Electron. J. Differential Equations. 2000(39):2000;1-17.
24. Popivanov P.R., Palagachev D.K. The Degenerate Oblique Derivative Problem for Elliptic and Parabolic Equations. 1997;Akademie, Berlin.
25. Sarason D. On functions of vanishing mean oscillation. Trans. Amer. Math. Soc. 207:1975;391-405.
26. Softova L.G. Oblique derivative problem for parabolic operators with VMO coefficients. Manuscripta Math. 103:2000;203-220.
27. L.G. Softova, Parabolic equations with VMO coefficients in Morrey spaces, Electron J. Differential Equations 2001 (51) (2001) 1-25, http://ejde.math.swt.edu/Volumes/2001/51.
28. Tomi F. Über semilineare elliptische Differentialgleichungen zweiter Ordnung. Math. Z. 111:1969;350-366.
29. Von Wahl W. Über quasilineare differentialgleichungen in der Ebene. Manuscripta Math. 8:1973;59-67.