Regularity for degenerate elliptic problems via p-harmonic approximation

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 21, Issue 5, 2004, Pages 735-766

  Duzaar, Frank ^a   Mingione, Giuseppe ^b  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

^b UNIVERSITY OF PARMA   (Italy)

Author keywords

p Laplacean; Partial regularity; Quasi convexity

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; CONFORMAL MAPPING; FUNCTIONS; HARMONIC ANALYSIS; INTEGRAL EQUATIONS; LAPLACE TRANSFORMS; MATHEMATICAL OPERATORS; SET THEORY; THEOREM PROVING;

DEGENERATE ELLIPTIC PROBLEMS; P-LAPLACEAN; PARTIAL REGULARITY; QUASI-CONVEXITY;

PROBLEM SOLVING;

EID: 4344636919     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpc.2003.09.003     Document Type: Article

References (21)

1. Acerbi E., Fusco N. Semicontinuity problems in the calculus of variations. Arch. Ration. Mech. Anal. 86:1984;125-145.
2. Acerbi E., Fusco N. A regularity theorem for minimizers of quasiconvex integrals. Arch. Ration. Mech. Anal. 99:1987;261-281.
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.
4. Acerbi E., Mingione G. Regularity results for stationary electro-rheological fluids. Arch. Ration. Mech. Anal. 164:2002;213-259.
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.
6. Duzaar F., Gastel A., Grotowski J. Partial regularity for almost minimizers of quasiconvex functionals. SIAM J. Math. Anal. 32:2000;665-687.
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.
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.
9. F. Duzaar, G. Mingione, The p -harmonic approximation and the regularity of p -harmonic maps, Calc. Var., 2004, in press.
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.
11. Evans L.C. Quasiconvexitity and partial regularity in the calculus of variations. Arch. Ration. Mech. Anal. 95:1986;227-252.
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.
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.
14. Grotowski J.F. Boundary regularity for nonlinear elliptic systems. Calc. Var. 15:2002;353-388.
15. Hamburger C. Regularity of differential forms minimizing degenerate elliptic functionals. J. Reine Angew. Math. 431:1992;7-64.
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.
17. Morrey C.B. Quasi-convexity and the lower semicontinuity of multiple integrals. Pacific J. Math. 2:1952;25-53.
18. Morrey C.B. Partial regularity results for non-linear elliptic systems. J. Math. Mech. 17:1967/1968;649-670.
19. Simon L. Lectures on Geometric Measure Theory. Proc. CMA. vol. 3:1983;ANU Canberra.
20. Simon L. Theorems on Regularity and Singularity of Energy Minimizing Maps. 1996;Birkhäuser-Verlag, Basel.
21. Šveràk V. Quasiconvex functions with subquadratic growth. Proc. Roy. Soc. London Ser. A. 433:1991;723-725.