The singular set of solutions to non-differentiable elliptic systems

Archive for Rational Mechanics and Analysis

Volumn 166, Issue 4, 2003, Pages 287-301

  Mingione, Giuseppe ^a  

^a UNIVERSITY OF PARMA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038610614     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00205-002-0231-8     Document Type: Article

References (22)

1. ACERBI, E., FUSCO, N.: Regularity for minimizers of nonquadratic functional: the case 1 < p < 2. J. Math. Anal. Appl. 140, 115-135 (1989)
2. ACERBI, E., MINGIONE, G.: Regularity results for stationary electro-rheological fluids. Arch. Rational Mech. Anal. 164, 213-259 (2002)
3. ADAMS, R.A.: Sobolev Spaces. New York: Academic Press, 1975
4. ADAMS, D.R., HEDBERG, L.I.: Function spaces and potential theory. Berlin: Springer-Verlag, 1996
5. CAMPANATO, S.: Hölder continuity of the solutions of some nonlinear elliptic systems. Adv. in Math. 48, 16-43 (1983)
6. DE GIORGI, E.: Un esempio di estremali discontinue per un problema variazionale di tipo ellittico. Boll. Un. Mat. Ital. 1, 135-137 (1968)
7. DUZAAR, F., GROTOWSKI, J.: Optimal interior partial regularity for nonlinear elliptic systems: the method of A-harmonic approximation. Manuscripta Math. 103, 267-298 (2000)
8. EVANS, L.C.: Quasiconvexity and partial regularity in the Calculus of Variations. Arch. Rational Mech. Anal. 95, 227-252 (1984)
9. EVANS, L.C., GARIEPY, R.: Blow-up, compactness and partial regularity in the Calculus of Variations. Indiana Univ. Math. J. 36, 361-371 (1987)
10. GIAQUINTA, M.: Multiple integrals in the Calculus of Variations and nonlinear elliptic systems. Annals of Mathematics Studies, 105 Princeton: Princeton University Press, 1983
11. GIAQUINTA, M., MODICA, G.: Almost-everywhere regularity for solutions of nonlinear elliptic systems. Manuscripta Math. 28, 109-158 (1979)
12. GIUSTI, E.: Metodi Diretti nel Calcolo delle Variazioni. UMI, Bologna, 1994
13. 1, p e singolarità delle soluzioni deboli di sistemi ellittici non lineari. Boll. Un. Mat. Ital. 2, 71-76 (1969)
14. GIUSTI, E., MIRANDA, M.: Sulla regolarità delle soluzioni deboli di una classe di sistemi ellittici quasi-lineari. Arch. Rational Mech. Anal. 31, 173-184 (1968/1969)
15. HAMBURGER, C.: A new partial regularity proof for solutions of nonlinear elliptic systems. Manuscripta Math. 95, 11-31 (1998)
16. IVERT, P.A.: Regularitätsuntersuchungen von lösungen elliptiscer systeme von quasilinearen differetialgléichungen zweiter ordnung. Manuscripta Math. 30, 53-88 (1979)
17. JOHN, O., MALÝ, J., STARÁ, J: Nowhere continuous solutions to elliptic systems. Comment. Math. Univ. Carolin. 30, 33-43 (1989)
18. MAZÝA, V.G.: Examples of irregular solutions of quasilinear elliptic equations with analytic coefficients. Funct. Anal. Appl. 2, 230-234 (1968)
19. MORREY JR. C.B.: Partial regularity results for non-linear elliptic systems. J. Math. Mech. 17, 649-670 (1967/1968)
20. STREDULINSKY, E.W.: Higher integrability from reverse Hölder inequalities. Indiana Univ. Math. J. 29, 407-413 (1980)
21. SVERÀK, V., YAN, X.: Non Lipschitz minimizers of smooth uniformly convex variational integrals. Proc. Nat. Ac. Sci. USA, to appear
22. UHLENBECK, K.: Regularity for a class of nonlinear elliptic systems. Acta Math. 138, 219-240 (1977)