Mixed boundary value problems for nonlinear elliptic systems in n-dimensional lipschitzian domains

Zeitschrift für Analysis und ihre Anwendungen

Volumn 18, Issue 3, 1999, Pages 539-555

  Ebmeyer, C ^a  

^a UNIVERSITY OF BONN   (Germany)

Author keywords

Mixed boundary value problems; Nikolskii spaces; Piecewise smooth boundaries

Indexed keywords

EID: 22844456205     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: 10.4171/ZAA/897     Document Type: Article

References (17)

1. Adams, R. A.: Sobolev Spaces, New York et al.: Academic Press 1975.
2. Banasiak, J.: On asymptotics of solutions of elliptic mixed boundary value problems of second-order in domains with vanishing edges. Siam J. Math. Anal. 23 (1992), 1117-1124.
3. Banasiak, J.: A counterexample in the theory of mixed boundary value problems for elliptic equations in non-smooth domains. Demonstr. Math. 26 (1993), 327-335.
4. Banasiak, J. and G. F. Roach: On mixed boundary value problems of Dirichlet oblique-derivative type in plane domains with piecewise differentiate boundary. J. Diff. Equ. 79 (1989), 111-131.
5. Borsuk, M. V.: Estimates of solutions of the Dirichlet problem for a quasilinear nondivergence elliptic equation of second order near a corner boundary point. St. Petersbg. Math. J. 3 (1992), 1281-1302.
6. Borsuk, M. V.: Behaviour of solutions of the Dirichlet problem for a second-order quasilinear elliptic equation of general form close to a corner point. Ukr. Math. J. 44 (1992), 149-155.
7. Dauge, M.: Elliptic Boundary Value Problems on Corner Domains. Lcct. Notes Math. 1341 (1988), 1-257.
8. Ebmeyer, C. and J. Frehse: Mixed boundary value problems for nonlinear elliptic equations in multidimensional non-smooth domains. Math. Nachr. 203 (1999) (to appear).
9. Grisvard, P.: Elliptic Problems in Nonsmooth Domains (Pitman Advanced Publishing Program). Boston - London - Melbourne: Pitman 1985.
10. Grisvard, P.: Edge behavior of the solution of an elliptic problem. Math. Nachr. 132 (1987), 281-299.
11. Kondrat'ev, V. A.: Boundary value problems for elliptic equations in domains with conical and angular points. Trans. Moscow Math. Soc. 16 (1967), 227-313.
12. Koslov, V. and V. Maz'ya: Angle singularities of solutions to the Neumann problem for the two-dimensional Riccati's equation. Asymptotic Anal. 19 (1999), 57-79.
13. Ladyzhenskaya, O. A. and N. N.Uraltseva: Linear and Quasilinear Elliptic Equations. New York - London: Acad. Press 1968.
14. Maz'ja, V. and J. Rossmann: On the behaviour of solutions to the Dirichlet problem for second order elliptic equations near edges and polyhedral vertices with critical angles. Z. Anal. Anw. 13 (1994), 19-47.
15. Miersemann, E.: Asymptotic expansions of solutions of the Dirichlet problem for quasilinear elliptic equations of second order near a conical point. Math. Nachr. 135 (1988), 239-274.
16. Morrey, C. B.: Multiple Integrals in the Calculus of Variations. Berlin - Heidelberg - New York: Springer-Verlag 1966.
17. PetersdorfT, T. v. and E. P. Stephan: Decompositions in edge and corner singularities for the solution of the Dirichlet problem of the Laplacian in a polyhedron. Math. Nachr. 149 (1990), 71-104.