Abstract
For certain quasilinear elliptic systems with perturbations of natural growth we prove a Caccioppoli-inequality provided the perturbation satisfies an additional “angle condition.” As a consequence weak solutions of these systems have the Hölder-continuity properties established by the so called direct approach to regularity, cf.: [2].
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Frehse J.: On a class of nonlinear diagonal elliptic systems with critical growth and Cα-regularity. In: Partial Differential Equations and the Calculus of Variations, ed. F. Colombini et al. Birkhäuser, Boston; (1989)
Giaquinta, M.: Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. Princeton University Press, Princeton, NJ; (1983)
Hildebrandt, S., Widman, K.-0.: On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order. Ann. Sc. Norm. Sup. Pisa, 4, 145–178 (1977)
Landes, R.: Testfunctions for elliptic systems and maximum principles. Forum Mathematicum 12, 23–52 (2000)
Wiegner, M.: Ein optimaler Regularitätssatz für schwache Lö sungen gewisser elliptischer Systeme, Math. Z. 147, 21–28 (1976)
Wiegner, M.: Das Existenz und Regularitätsproblem bei Systemen nichtlinearer elliptischer Differentialgleichungen, Habilitationsschrift, Bochum, (1977)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Landes, R. On the regularity of weak solutions of certain elliptic systems. Calc. Var. 25, 247–255 (2006). https://doi.org/10.1007/s00526-005-0360-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00526-005-0360-7