Abstract

The authors continue the study of regularity properties for solutions of elliptic systems started by M. A. Ragusa [(1) Local Hölder regularity for solutions of elliptic systems, Duke Mathematical Journal 113 (2002) 385–397; (2) Continuity of the derivatives of solutions related to elliptic equations, Proc. Royal Society of Edinburgh 136(A) (2006) 1027–1039], proving, in a bounded open set Ω\Omega of Rn{\mathbb R}^n, local differentiability and partial Hölder continuity of the weak solutions uu of nonlinear elliptic systems of order 2m2m in divergence form ∑∣α∣≤m(−1)∣α∣Dα aα(x,Du)=0.\sum_{|\alpha|\leq m}(-1)^{|\alpha|} D^\alpha \, a^\alpha (x, Du) = 0. Specifically, we generalize the results obtained by S. Campanato and P. Cannarsa [Differentiability and partial Hölder continuity of the solutions of nonlinear elliptic systems of order 2m2m with quadratic growth, Ann. Scuola Norm. Sup. Pisa (4)8 (1981) 285–309] under the hypothesis that the coefficients aα(x,Du)a^\alpha (x, Du) are strictly monotone with nonlinearity q=2q = 2.

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Giuseppe Floridia

Dip. di Matematica e Informatica, Università di Catania, Viale A. Doria 6, 95125 Catania, Italy

floridia@dmi.unict.it

Maria Alessandra Ragusa

Dip. di Matematica e Informatica, Università di Catania, Viale A. Doria 6, 95125 Catania, Italy

maragusa@dmi.unict.it

Keywords

  • Higher order nonlinear elliptic systems
  • divergence form
  • monotone coefficients
  • generalized Sobolev spaces
  • local differentiability

Mathematics Subject Classification

35J48, 35D10; 35J45, 35D30

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Suggested citation

G. Floridia, M. A. Ragusa. “Differentiabilty and Partial Hölder Continuity of Solutions of Nonlinear Elliptic Systems.” Journal of Convex Analysis 19 (2012), No. 1, 63–90. https://doi.org/10.68381/jca19004

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Published by Heldermann Verlag, 2012. Rights now held by Banach Press LLC.