Regularity for degenerate elliptic problems via $p$-harmonic approximation

Duzaar, Frank; Mingione, Giuseppe

doi:10.1016/j.anihpc.2003.09.003

Regularity for degenerate elliptic problems via

p

-harmonic approximation

Duzaar, Frank; Mingione, Giuseppe

Annales de l'I.H.P. Analyse non linéaire, Volume 21 (2004) no. 5, p. 735-766

Zbl 02116187 | 3 citations in Numdam

DOI : https://doi.org/10.1016/j.anihpc.2003.09.003

@article{AIHPC_2004__21_5_735_0,
     author = {Duzaar, Frank and Mingione, Giuseppe},
     title = {Regularity for degenerate elliptic problems via $p$-harmonic approximation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {21},
     number = {5},
     year = {2004},
     pages = {735-766},
     doi = {10.1016/j.anihpc.2003.09.003},
     zbl = {02116187},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2004__21_5_735_0}
}

Duzaar, Frank; Mingione, Giuseppe. Regularity for degenerate elliptic problems via $p$-harmonic approximation. Annales de l'I.H.P. Analyse non linéaire, Volume 21 (2004) no. 5, pp. 735-766. doi : 10.1016/j.anihpc.2003.09.003. http://www.numdam.org/item/AIHPC_2004__21_5_735_0/

References

[1] Acerbi E., Fusco N., Semicontinuity problems in the calculus of variations, Arch. Ration. Mech. Anal. 86 (1984) 125-145. | MR 751305 | Zbl 0565.49010

[2] Acerbi E., Fusco N., A regularity theorem for minimizers of quasiconvex integrals, Arch. Ration. Mech. Anal. 99 (1987) 261-281. | MR 888453 | Zbl 0627.49007

[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. | MR 997847 | Zbl 0686.49004

[4] Acerbi E., Mingione G., Regularity results for stationary electro-rheological fluids, Arch. Ration. Mech. Anal. 164 (2002) 213-259. | MR 1930392 | Zbl 1038.76058

[5] Carozza M., Fusco N., Mingione G., Partial regularity of minimizers of quasiconvex integrals with subquadratic growth, Ann. Mat. Pura Appl. IV 175 (1998) 141-164. | MR 1748219 | Zbl 0960.49025

[6] Duzaar F., Gastel A., Grotowski J., Partial regularity for almost minimizers of quasiconvex functionals, SIAM J. Math. Anal. 32 (2000) 665-687. | MR 1786163 | Zbl 0989.49026

[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. | MR 1802484 | Zbl 0971.35025

[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. | Zbl 05058521

[9] F. Duzaar, G. Mingione, The p-harmonic approximation and the regularity of p-harmonic maps, Calc. Var., 2004, in press. | MR 2062943 | Zbl 02123229

[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. | MR 1900994 | Zbl 0999.49024

[11] Evans L.C., Quasiconvexitity and partial regularity in the calculus of variations, Arch. Ration. Mech. Anal. 95 (1986) 227-252. | MR 853966 | Zbl 0627.49006

[12] Fusco N., Hutchinson J.E., Partial regularity for minimisers of certain functionals having nonquadratic growth, Ann. Mat. Pura Appl. IV 155 (1989) 1-24. | MR 1042826 | Zbl 0698.49001

[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. | MR 235264 | Zbl 0167.10703

[14] Grotowski J.F., Boundary regularity for nonlinear elliptic systems, Calc. Var. 15 (2002) 353-388. | MR 1938819 | Zbl 01883394

[15] Hamburger C., Regularity of differential forms minimizing degenerate elliptic functionals, J. Reine Angew. Math. 431 (1992) 7-64. | MR 1179331 | Zbl 0776.35006

[16] Kronz M., Partial regularity results for minimizers of quasiconvex functionals of higher order, Ann. Inst. Henri Poincaré, Analyse non linéaire 19 (2002) 81-112. | Numdam | MR 1902546 | Zbl 1010.49023

[17] Morrey C.B., Quasi-convexity and the lower semicontinuity of multiple integrals, Pacific J. Math. 2 (1952) 25-53. | MR 54865 | Zbl 0046.10803

[18] Morrey C.B., Partial regularity results for non-linear elliptic systems, J. Math. Mech. 17 (1967/1968) 649-670. | MR 237947 | Zbl 0175.11901

[19] Simon L., Lectures on Geometric Measure Theory, Proc. CMA, vol. 3, ANU Canberra, 1983. | MR 756417 | Zbl 0546.49019

[20] Simon L., Theorems on Regularity and Singularity of Energy Minimizing Maps, Birkhäuser-Verlag, Basel, 1996. | MR 1399562 | Zbl 0864.58015

[21] Šveràk V., Quasiconvex functions with subquadratic growth, Proc. Roy. Soc. London Ser. A 433 (1991) 723-725. | MR 1116970 | Zbl 0741.49016