We consider higher order quasimonotone nonlinear systems of divergence type with growth of order , , and Dini continuous coefficients. Using the technique of harmonic approximation we give a direct partial regularity proof for weak solutions.
Consideriamo sistemi nonlineari quasimonotoni di tipo di divergenza di ordine alto con crescenza di ordine , e coefficienti di Dini continui. Usando la tecnica dell'approssimazione armonica, diamo una dimostrazione diretta per la regolarità parziale di soluzioni deboli.
@article{BUMI_2003_8_6B_2_459_0, author = {Manfred Kronz}, title = {Quasimonotone systems of higher order}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {6-A}, year = {2003}, pages = {459-480}, zbl = {1150.35385}, mrnumber = {1988216}, language = {en}, url = {http://dml.mathdoc.fr/item/BUMI_2003_8_6B_2_459_0} }
Kronz, Manfred. Quasimonotone systems of higher order. Bollettino dell'Unione Matematica Italiana, Tome 6-A (2003) pp. 459-480. http://gdmltest.u-ga.fr/item/BUMI_2003_8_6B_2_459_0/
[C1] Proprietà di una famiglia di spazi funzionali, Ann. Scuola Norm. Sup. Pisa 18 (1964), 137-160. | MR 167862 | Zbl 0133.06801
,[C2] Teoremi di interpolazione per tranformazioni che applicano in , Ann. Scuola Norm. Sup. Pisa, 18 (1964), 345-360. | MR 170202 | Zbl 0135.35102
,[C3] Equazioni ellitichi del IIe ordine e spazi , Ann. Mat. Pura Appl., 69 (1965), 321-381. | MR 192168 | Zbl 0145.36603
,[C4] Alcune osservazioni relative alle soluzioni di equazioni ellittiche di ordine , Atti Convegno Equaz. Der. Parz., Bologna, 1967, 17-25. | MR 264207
,[DS] Optimal interior and boundary regularity for almost minimizers to elliptic variational integrals, Preprint. | MR 1900994 | Zbl 0999.49024
- ,[DGG] Optimal partial regularity for nonlinear elliptic systems of higher order, Preprint. | MR 1855456 | Zbl 0995.35017
- - ,[E] Quasiconvexitity and Partial Regularity in the Calculus of Variations, Arch. Rat. Mech. Anal., 95 (1986), 227-252. | MR 853966 | Zbl 0627.49006
,[F] Regularity theorems for nonlinear systems of partial differential equations under natural ellipticity conditions, Analysis7 (1987), 83-93. | MR 885719 | Zbl 0624.35032
,[Gi] | MR 1239172 | Zbl 0786.35001
, Introduction to Regularity Theory for Nonlinear Elliptic Systems, Basel-Boston-Berlin, Birkhäuser, 1993.[Gu] A Remark on Partial Regularity of Minimizers of Quasiconvex Integrals of Higher Order, Rend. Istit. Mat. Univ. Trieste, 32 (2000), 1-24. | MR 1828559 | Zbl 1006.49028
,[GM1] Almost-everywhere regularity results for solutions of nonlinear elliptic systems, Manuscripta Math., 28 (1979), 109-158. | MR 535699 | Zbl 0411.35018
- ,[GM2] Partial regularity of minimizers of quasiconvex integrals, Ann. Inst. Henri Poincaré, Analyse non linéaire, 3 (1986), 185-208. | MR 847306 | Zbl 0594.49004
- ,[H] Quasimonotonicity, regularity and duality for nonlinear systems of partial differential equations, Ann. Mat. Pura Appl., IV. Ser., 169 (1995), 321-354. | MR 1378480 | Zbl 0852.35031
,[K] Partial Regularity Results for Quasiconvex Functionals of Higher Order, Ann. Inst. Henri Poincaré, Analyse non linéaire, 19 (2002), 81-112. | MR 1902546 | Zbl 1010.49023
,[M] Quasi-Convexity and Lower Semi-Continuity of Multiple Variational Integrals of Any Order, Trans. Am. Math. Soc., 119 (1965), 125-149. | MR 188838 | Zbl 0166.38501
,[S] | MR 1399562 | Zbl 0864.58015
, Theorems on Regularity and Singularity of Energy Minimizing Maps, Basel-Boston-Berlin, Birkhäuser, 1996.[Z] On the Dirichlet problem for a class of quasilinear elliptic systems of partial differential equations in divergence form, Partial differential equations, Proc. Symp., Tianjin/China, 1986, Lect. Notes Math., 1306 (1988), 262-277. | MR 1032785 | Zbl 0672.35026
,