The p-harmonic approximation and the regularity of p-harmonic maps

Calculus of Variations and Partial Differential Equations

Volumn 20, Issue 3, 2004, Pages 235-256

  Duzaar, Frank ^a   Mingione, Giuseppe ^b  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

^b UNIVERSITY OF PARMA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3042673947     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00526-003-0233-x     Document Type: Article

References (19)

1. Acerbi, E., Fusco, N.: Semicontinuity problems in the calculus of variations. Arch. Rational Mech. Anal. 86, 125-145 (1984)
2. Acerbi, E., Fusco, N.: Regularity for minimizers of non-quadratic functionals: the case 1 < p < 2. J. Math. Anal. Appl. 140, 115-135 (1989)
3. 2,λ Ann. Mat. Pura Appl. IV. Ser. 69, 321-380 (1965)
4. De Giorgi, E.: Frontiere orientate di misura minima. Seminario di Matematica, Scu. Norm. Sup. Pisa (1960-1961)
5. Duzaar, F., Mingione, G.: Regularity for degenerate elliptic problems via p-harmonic approximation. Preprint Dip. Mat. Univ. Parma No. 326, May 2003
6. Eisen, G.: A selection lemma for sequences of measurable sets, and lower semicontinuity of multiple integrals. Manuscripta Math. 27, 73-79 (1979)
7. Frerhse, J., Málek, J., Steinhauer, M.: On analysis of steady flows of fluids with sheardependent viscosity based on the Lipschitz truncation method. SIAM J. Math. Anal. 34, 1064-1083 (2003)
8. Fuchs, M.: p-harmonic obstacle problems. I: Partial regularity theory. Ann. Mat. Pura Appl., IV. Ser. 156, 127-158 (1990)
9. Fusco, N., Hutchinson, J.: Partial regularity for minimisers of certain functionals having nonquadratic growth. Ann. Mat. Pura Appl. IV. Ser. 155, 1-24 (1989)
10. Giaquinta, M., Modica, G.: Remarks on the regularity of the minimizers of certain degenerate functionals. Manuscripta Math. 57, 55-99 (1986)
11. p norm of the gradient. Comm. Pure Appl. Math. 40, 555-588 (1987)
12. Hardt, R., Lin, F.H., Mou, L.: Strong convergence of p-harmonic mappings. In: Chipot, M. (ed.) et al., Progress in partial differential equations: the Metz surveys 3. Proceedings of the conferences given at the University of Metz, France during the 1993 "Metz Days". Harlow: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 314, 58-64 (1994)
13. Luckhaus, S.: Partial Hölder continuity for minima of certain energies among maps into Riemannian manifold. Indiana Univ. Math. J. 37, 349-367 (1988)
14. Schoen, R., Uhlenbeck, K.: A regularity theory for harmonic maps. J. Differential Geom. 17, 307-336 (1982)
15. Schoen, R., Uhlenbeck, K.: Boundary regularity and the Dirichlet problem for harmonic maps. J. Differential Geom. 18, 253-268 (1983)
16. Simon, L.: Lectures on geometric measure theory. Proc. CMA 3, ANU Canberra 1983
17. Simon, L.: Theorems on regularity and singularity of energy minimizing maps. Birkhäuser-Verlag, Basel-Boston-Berlin 1996
18. Tolksdorf, P.: Everywhere-regularity for some quasilinear systems with a lack of ellipticity. Ann. Mat. Pura Appl., IV. Ser. 134, 241-266 (1983)
19. Uhlenbeck, K.: Regularity for a class of nonlinear elliptic systems. Acta Math. 138, 219-240 (1977)