Abstract

We consider the partial Hölder continuity of minimizers of functionals of the form v↦∫Ωf(x,v,Dv) dx,v\mapsto\int_{\Omega}f(x,v,Dv)\ dx, where Ω⊆Rn\Omega\subseteq\mathbb{R}^n is open and bounded. In our setting the integrand f ⁣:Ω×RN×RN×n→Rf\colon \Omega\times\mathbb{R}^N\times \mathbb{R}^{N\times n}\rightarrow\mathbb{R} is not necessarily continuous in any of its three arguments. In particular, due to the use of a suitable asymptotic relatedness condition, ff possesses continuity and convexity only as the norm of its third argument tends to infinity. Since, in particular, vv is possibly vector-valued, this provides a generalization of certain existing regularity results in the literature and helps to further build a low-order regularity theory.

Author information

Contact details are reproduced from the original publication and may be historical.

Mikil Foss

Dept. of Mathematics, University of Nebraska, Lincoln, NE 68588, U.S.A.

mfoss2@math.unl.edu

Christopher S. Goodrich

Dept. of Mathematics, Creighton Preparatory School, Omaha, NE 68114, U.S.A.
and: Dept. of Mathematics, University of Rhode Island, Kingston, RI 02881, U.S.A.

cgood@prep.creighton.edu

Keywords

  • Partial regularity
  • Morrey regularity
  • Hölder continuity

Mathematics Subject Classification

49N60; 46E35

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Suggested citation

M. Foss, C. S. Goodrich. “Partial Hölder Continuity of Minimizers of Functionals Satisfying a General Asymptotic Relatedness Condition.” Journal of Convex Analysis 22 (2015), No. 1, 219–246. https://doi.org/10.68381/jca22011

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