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Article

Keywords:
nonlinear elliptic systems; regularity up to the boundary
Summary:
Regularity results for elliptic systems of second order quasilinear PDEs with nonlinear growth of order $q>2$ are proved, extending results of [7] and [10]. In particular Hölder regularity of the solutions is obtained if the dimension $n$ is less than or equal to $q + 2$.
References:
[1] S. Campanato: Equazioni ellittiche del secondo ordine e spazi $L^{2, \lambda }$. Ann. Mat. Pura e Appl. 69 (1965), 321–381. DOI 10.1007/BF02414377 | MR 0192168
[2] S. Campanato: Sistemi ellittici in forma di divergenza. Regolarità all’interno. Quaderni S.N.S. di Pisa, 1980. MR 0668196
[3] S. Campanato: Elliptic systems with nonlinearity  $q$ greater or equal to two. Regularity of the solution of the Dirichlet Problem. Ann. Mat. Pura e Appl. 147 (1987), 117–150. DOI 10.1007/BF01762414 | MR 0916705 | Zbl 0635.35038
[4] S. Campanato: A maximum principle for nonlinear elliptic systems. Boundary fundamental estimates. Advances in Math. 66 (1987), 291–317. DOI 10.1016/0001-8708(87)90037-5 | MR 0915857 | Zbl 0644.35042
[5] S. Campanato: A maximum principle for nonlinear elliptic systems. Atti Convegno commem. di M. Picone e L. Tonelli vol. , Acc. Lincei, Roma, 1985, pp. 173–182.
[6] E. De Giorgi: Un esempio di estremali discontinue per un problema variazionale di tipo ellittico. Boll. Un. Mat. Ital. 1 (1968), 135–137. MR 0227827
[7] L. Fattorusso, G. Idone: Hölder regularity for nonlinear nonhomogeneous elliptic systems. Le Matematiche 50 (1995), 285–306. MR 1414636
[8] J. Frehse: On the boundedness of weak solutions of higher order nonlinear elliptic partial differential equations. Boll. Un. Mat. Ital. 4 (1970), 607–627. MR 0274938 | Zbl 0203.41303
[9] J. Serrin: Local behaviour of solutions of quasilinear equations. Acta Math. 111 (1964), 247–302. DOI 10.1007/BF02391014 | MR 0170096
[10] K. Widman: Hölder continuity of solutions of elliptic systems. Manuscripta Math. 5 (1971), 299–308. DOI 10.1007/BF01367766 | MR 0296484 | Zbl 0223.35044
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