Solutions for Quasilinear Nonsmooth Evolution Systems in Lp

Archive for Rational Mechanics and Analysis

Volumn 171, Issue 2, 2004, Pages 219-262

  Maz'ya, V ^a   Elschner, J ^b   Rehberg, J ^b   Schmidt, G ^b  

^a LINKÖPING UNIVERSITY   (Sweden)

^b WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1142300772     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00205-003-0297-y     Document Type: Article

References (33)

1. AMANN, H.: Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems. In: Function spaces, differential operators and nonlinear analysis, H.-J. SCHMEISSER et al., (ed.), Teubner-Texte Math., Vol. 133, Stuttgart, 1993, pp. 9-126
2. ANTONTSEV, S.N., CHIPOT, M.: The thermistor problem: Existence, smoothness, uniqueness, blowup. SIAM J. Math. Anal. 25, 1128-1156 (1994)
3. CIARLET, P.O.: The finite element method for elliptic problems. Studies in Mathematics and its Applications, North Holland, Amsterdam, New York, Oxford, 1979
4. COIFMAN, R.R., MEYER, Y.: Au delà des opérateurs pseudodifférentiels. Asterisque 57, 2-185 (1978)
5. COSTABEL, M., DAUGE, M., LAFRANCHE, Y: Fast semi-analytic computation of elastic edge singularities. Comput. Meth. Appl. Mech. Engrg. 190, 2111-2134 (2001)
6. FILA, M., MATANO, H.: Blow up in nonlinear heat equations from the dynamical systems point of view. In: Handbook of Dynamical Systems, Vol. 2, B. FIEDLER (ed.), Elsevier, 2002
7. GAJEWSKJ, H.: Analysis und Numerik von Ladungstransport in Halbleitern. Mitt. Ges. Angew. Math. Mech. 16, 35-57 (1993)
8. GAJEWSKI, H., GRÖGER, K., ZACHARIAS, K.: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. Akademie-Verlag, 1974
9. GIAQUINTA, M., MODICA, G.: Local existence for quasilinear parabolic systems under nonlinear boundary conditions. Ann. Mat. Pura Appl. 149, 41-59 (1987)
10. GELBARG, D., TRUDINGER, N.S.: Elliptic partial differential equations of second order. Springer, New York, 1983
11. GRACHEV, N.V., MAZ'YA, V.G.: A contact problem for the Laplace equation in the exterior of the boundary of a dihedral angle. Math. Nachr. 151, 207-231 (1991) (Russian)
12. P. Adv. Math. Sci. Appl. 11, 87-112 (2001)
13. GRIEPENTROG, J.A., GRÖGER, K., KAISER, H.C., REHBERG, J.: Interpolation for function spaces related to mixed boundary value problems. Math. Nachr. 241, 110-120 (2002)
14. IL'IN, E.M.: Singularities of the weak solutions of elliptic equations with discontinuous higher coefficients. II. Corner points of the lines of discontinuity. Zap. Nauchn. Semin. LOMI 47, 166-169 (1974) (Russian)
15. JERISON, D., KENIG, C.: The inhomogeneous Dirichlet problem in Lipschitz domains. J. Fund. Anal. 130, 161-219 (1995)
16. KELLOGG, R.B.: On the Poisson equation with intersecting interfaces. Appl. Anal. 4, 101-129 (1975)
17. KONDRATIEV, V.A.: Boundary problems for elliptic equations in domains with conical or angular points. Trans. Moscow Math. Soc. 16, 227-313 (1967)
18. KOZLOV, VA., MAZ'YA, V.G.: Differential equations with operator coefficients. Springer, Berlin, 1999
19. KOZLOV, V.A., MAZ'YA, V.G., ROSSMANN, J.: Elliptic boundary value problems in domains with point singularities. Mathem. Surveys and Monographs, Vol. 52, Amer. Math. Soc., Providence, 1997
20. KOZLOV, V.A., MAZ'YA, V.G., ROSSMANN, J.: Spectral problems associated with corner singularities of solutions to elliptic equations. Mathem. Surveys and Monographs, Vol. 85, Amer. Math. Soc., Providence, 2001
21. LADYZHENSKAYA, O.A., SOLONNIKOV, V.A., URAL'TSEVA, N.M.: Linear and quasilinear equations of parabolic type. AMS Transl. Math., Rhode Island, 1968
22. MAZ'YA, V.O., PLAMENEVSKII, B.A.: The first boundary value problem for classical equations of mathematical physics in domains with piecewise smooth boundaries, I. Z. Anal. Anwend. 2, 335-359 (1983) (Russian)
23. MAZ'YA, V.O., PLAMENEVSKII, B.A.: The first boundary value problem for classical equations of mathematical physics in domains with piecewise smooth boundaries, II. Z. Anal. Anwend. 2, 523-551 (1983) (Russian)
24. MAZ'YA, V.O., ROSSMANN, J.: Point estimates for Green's matrix to boundary value problems for second order elliptic systems in a polyhedral cone. ZAMM 82, 291-316 (2002)
25. PETZOLDT, M: Regularity results for Laplace interface problems in two dimensions. Z. Anal. Anwend. 20, 431-455 (2001)
26. ROITBERG, J.A., SHEFTEL, Z.G.: On equations of elliptic type with discontinuous coefficients. Sou Math. Dokl. 3, 1491-1494 (1962)
27. SCHECHTER, M.: A generalization of the problem of transmission. Ann. Scuola Norm. Sup. Pisa 14, 207-236 (1960)
28. SOBOLEVSKII, P.E.: Equations of parabolic type in a Banach space. In: Amer. Math. Soc. Transl. 49, Providence, 1964, pp. 1-62
29. SOMMERFELD, A.: Thermodynamics and statistical mechanics. Lectures on theoretical physics, Vol. V, Academic Press, New York, 1956
30. STAMPACCHIA, G.: Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier 15, 189-257 (1965)
31. STRUWE, M.: On the Hoelder continuity of bounded weak solutions of quasilinear systems. Manuscr. Math. 35, 125-145 (1981)
32. TRIEBEL, H.: Interpolation theory, function spaces, differential operators. North Holland Publishing Company, 1978
33. WIEGNER, M.: Global solutions to a class of strongly coupled parabolic systems. Math. Ann. 292, 711-727 (1992)