Abstract
We minimize the Dirichlet-integral in a class of vector-valued functions u:Ω→ℝN defined by Dirichlet-boundary conditions and a side-condition of the form u(ω)⊂M with M bounded and open in ℝN having smooth boundary ∂M. If the boundary values are sufficiently regular we show that the minimizer can only have interior singularities, i.e. the solution is smooth in a neighborhood of ∂Ω.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Duzaar, F.; Fuchs, M. Variational problems with non-convex obstacles and an integral constraint for vector-valued functions to appear
Giaquinta, M.; Giusti,E. On the regularity of minima of variational integrals Acta Math. 148, 31–46 (1982)
Giaquinta, M.; Giusti,E On the singular set of the minima of certain quadratic functionals preprint 453 SFB 72 Bonn
Giaquinta, M.; Giusti,E. Differentiability of minima of non-differentiable functionals Inv.Math. 72, 285–298 (1983)
Jost, J.; Meier, M. Boundary regularity for minima of certain quadratic functionals Math.Ann. 262, 549–561 (1983)
Wood, J.C. Non-existence of solutions to certain Dirichletproblems preprint, Leeds 1981
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fuchs, M. Some remarks on the boundary regularity for minima of variational problems with obstacles. Manuscripta Math 54, 107–119 (1985). https://doi.org/10.1007/BF01171702
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01171702