Kronz, Manfred:
Quasimonotone systems of higher order
Bollettino dell'Unione Matematica Italiana Serie 8 6-B (2003), fasc. n.2, p. 459-480, Unione Matematica Italiana (English)
pdf (327 Kb), djvu (276 Kb). | MR1988216 | Zbl 1150.35385
Sunto
Consideriamo sistemi nonlineari quasimonotoni di tipo di divergenza di ordine alto con crescenza di ordine $p$, $p\geq 2$ e coefficienti di Dini continui. Usando la tecnica dell'approssimazione armonica, diamo una dimostrazione diretta per la regolarità parziale di soluzioni deboli.
Referenze Bibliografiche
[C2]
S. CAMPANATO,
Teoremi di interpolazione per tranformazioni che applicano $L^p$ in $C^{h,\alpha}$,
Ann. Scuola Norm. Sup. Pisa,
18 (
1964), 345-360. |
fulltext mini-dml |
MR 170202 |
Zbl 0135.35102[C3]
S. CAMPANATO,
Equazioni ellitichi del IIe ordine e spazi $\mathcal{L}^{2,\lambda}$,
Ann. Mat. Pura Appl.,
69 (
1965), 321-381. |
MR 192168 |
Zbl 0145.36603[C4]
S. CAMPANATO,
Alcune osservazioni relative alle soluzioni di equazioni ellittiche di ordine $2m$,
Atti Convegno Equaz. Der. Parz., Bologna,
1967, 17-25. |
MR 264207[DS]
F. DUZAAR-
K. STEFFEN,
Optimal interior and boundary regularity for almost minimizers to elliptic variational integrals, Preprint. |
MR 1900994 |
Zbl 0999.49024[DGG]
F. DUZAAR-
A. GASTEL-
J. GROTOWSKI,
Optimal partial regularity for nonlinear elliptic systems of higher order, Preprint. |
MR 1855456 |
Zbl 0995.35017[E]
L. C. EVANS,
Quasiconvexitity and Partial Regularity in the Calculus of Variations,
Arch. Rat. Mech. Anal.,
95 (
1986), 227-252. |
MR 853966 |
Zbl 0627.49006[F]
M. FUCHS,
Regularity theorems for nonlinear systems of partial differential equations under natural ellipticity conditions,
Analysis 7 (
1987), 83-93. |
MR 885719 |
Zbl 0624.35032[Gi]
M. GIAQUINTA,
Introduction to Regularity Theory for Nonlinear Elliptic Systems, Basel-Boston-Berlin,
Birkhäuser,
1993. |
MR 1239172 |
Zbl 0786.35001[Gu]
M. GUIDORZI,
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]
M. GIAQUINTA-
G. MODICA,
Almost-everywhere regularity results for solutions of nonlinear elliptic systems,
Manuscripta Math.,
28 (
1979), 109-158. |
MR 535699 |
Zbl 0411.35018[GM2]
M. GIAQUINTA-
G. MODICA,
Partial regularity of minimizers of quasiconvex integrals,
Ann. Inst. Henri Poincaré, Analyse non linéaire,
3 (
1986), 185-208. |
fulltext mini-dml |
MR 847306 |
Zbl 0594.49004[H]
C. HAMBURGER,
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[M]
N. G. MEYERS,
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]
L. SIMON,
Theorems on Regularity and Singularity of Energy Minimizing Maps, Basel-Boston-Berlin,
Birkhäuser,
1996. |
MR 1399562 |
Zbl 0864.58015[Z]
KE-WEI ZHANG,
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
Con il contributo del Ministero per i Beni e le Attività Culturali