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Article

Fuchs, Martin
Smoothness for systems of degenerate variational inequalities with natural growth. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 33 (1992), issue 1, pp. 33-41
MSC: 35J85, 49J40 | MR 1173743 | Zbl 0773.49005
Keywords:
variational inequalities; regularity theory
Summary:
We extend a regularity theorem of Hildebrandt and Widman [3] to certain degenerate systems of variational inequalities and prove Hölder-continuity of solutions which are in some sense stationary.
References:
[1] Fuchs M., Fusco N.: Partial regularity results for vector valued functions which minimize certain functionals having nonquadratic growth under smooth side conditions. J. Reine Angew. Math. 399 (1988), 67-78. MR 0953677
[2] Giaquinta M.: Multiple integrals in the calculus of variations and nonlinear elliptic systems. Ann. of Math. Studies 105, Princeton U.P. 1983. MR 0717034 | Zbl 0516.49003
[3] Hildebrandt S., Widman K.-O.: Variational inequalities for vectorvalued functions. J. Reine Angew. Math. 309 (1979), 181-220. MR 0542048 | Zbl 0408.49012
[4] Price P.: A monotonicity formula for Yang-Mills fields. Manus. Math. 43 (1983), 131-166. MR 0707042 | Zbl 0521.58024
[5] Uhlenbeck K.: Regularity for a class of nonlinear elliptic systems. Acta Math. 138 (1977), 219-240. MR 0474389 | Zbl 0372.35030
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