Regularity for degenerate elliptic problems via p-harmonic approximation

 Access to full text

 Full (PDF)

1. [1] Acerbi E., Fusco N., Semicontinuity problems in the calculus of variations, Arch. Ration. Mech. Anal.86 (1984) 125-145. Zbl0565.49010MR751305
2. [2] Acerbi E., Fusco N., A regularity theorem for minimizers of quasiconvex integrals, Arch. Ration. Mech. Anal.99 (1987) 261-281. Zbl0627.49007MR888453
3. [3] Acerbi E., Fusco N., Regularity for minimizers of non-quadratic functionals: the case 1<p<2, J. Math. Anal. Appl.140 (1989) 115-135. Zbl0686.49004MR997847
4. [4] Acerbi E., Mingione G., Regularity results for stationary electro-rheological fluids, Arch. Ration. Mech. Anal.164 (2002) 213-259. Zbl1038.76058MR1930392
5. [5] Carozza M., Fusco N., Mingione G., Partial regularity of minimizers of quasiconvex integrals with subquadratic growth, Ann. Mat. Pura Appl. IV175 (1998) 141-164. Zbl0960.49025MR1748219
6. [6] Duzaar F., Gastel A., Grotowski J., Partial regularity for almost minimizers of quasiconvex functionals, SIAM J. Math. Anal.32 (2000) 665-687. Zbl0989.49026MR1786163
7. [7] Duzaar F., Grotowski J., Optimal interior partial regularity for nonlinear elliptic systems: the method of A-harmonic approximation, Manuscripta Math.103 (2000) 267-298. Zbl0971.35025MR1802484
8. [8] F. Duzaar, J. Grotowski, M. Kronz, Regularity of almost minimizers of quasi-convex integrals with subquadratic growth, Ann. Mat. Pura Appl., 2004, in press. Zbl1223.49040
9. [9] F. Duzaar, G. Mingione, The p-harmonic approximation and the regularity of p-harmonic maps, Calc. Var., 2004, in press. Zbl1142.35433MR2062943
10. [10] Duzaar F., Steffen K., Optimal interior and boundary regularity for almost minimizers to elliptic variational integrals, J. Reine Angew. Math.546 (2002) 73-138. Zbl0999.49024MR1900994
11. [11] Evans L.C., Quasiconvexitity and partial regularity in the calculus of variations, Arch. Ration. Mech. Anal.95 (1986) 227-252. Zbl0627.49006MR853966
12. [12] Fusco N., Hutchinson J.E., Partial regularity for minimisers of certain functionals having nonquadratic growth, Ann. Mat. Pura Appl. IV155 (1989) 1-24. Zbl0698.49001MR1042826
13. [13] Giusti E., Miranda M., Sulla regolaritá delle soluzioni deboli di una classe di sistemi ellittici quasi-lineari, Arch. Ration. Mech. Anal.31 (1968/1969) 173-184. Zbl0167.10703MR235264
14. [14] Grotowski J.F., Boundary regularity for nonlinear elliptic systems, Calc. Var.15 (2002) 353-388. Zbl1148.35315MR1938819
15. [15] Hamburger C., Regularity of differential forms minimizing degenerate elliptic functionals, J. Reine Angew. Math.431 (1992) 7-64. Zbl0776.35006MR1179331
16. [16] Kronz M., Partial regularity results for minimizers of quasiconvex functionals of higher order, Ann. Inst. Henri Poincaré, Analyse non linéaire19 (2002) 81-112. Zbl1010.49023MR1902546
17. [17] Morrey C.B., Quasi-convexity and the lower semicontinuity of multiple integrals, Pacific J. Math.2 (1952) 25-53. Zbl0046.10803MR54865
18. [18] Morrey C.B., Partial regularity results for non-linear elliptic systems, J. Math. Mech.17 (1967/1968) 649-670. Zbl0175.11901MR237947
19. [19] Simon L., Lectures on Geometric Measure Theory, Proc. CMA, vol. 3, ANU Canberra, 1983. Zbl0546.49019MR756417
20. [20] Simon L., Theorems on Regularity and Singularity of Energy Minimizing Maps, Birkhäuser-Verlag, Basel, 1996. Zbl0864.58015MR1399562
21. [21] Šveràk V., Quasiconvex functions with subquadratic growth, Proc. Roy. Soc. London Ser. A433 (1991) 723-725. Zbl0741.49016MR1116970

1. Jialin Wang, Dongni Liao, Zefeng Yu, Hölder continuity for sub-elliptic systems under the sub-quadratic controllable growth in Carnot groups
2. Mikil Foss, Giuseppe Mingione, Partial continuity for elliptic problems
3. Frank Duzaar, Giuseppe Mingione, Second order parabolic systems, optimal regularity, and singular sets of solutions
4. Giuseppe Mingione, Regularity of minima: an invitation to the Dark Side of the Calculus of Variations