Abstract

We develop a field theory for one-dimensional variational problems defined via integrands with low regularity and singular ellipticity. This is developed via a priori existence and regularity results for one-dimensional obstacle problems with such integrands.

Author information

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

Richard Gratwick

School of Mathematics, The University of Edinburgh, United Kingdom

r.gratwick@ed.ac.uk

Mikhail A. Sychev

Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russia

masychev@math.nsc.ru

Keywords

  • Integral functionals
  • obstacle problems
  • singular ellipticity
  • Tonelli regularity
  • existence and regularity in small
  • field theory

Mathematics Subject Classification

49N60

Suggested citation

R. Gratwick, M. A. Sychev. “Field Theory for Integrands with Low Regularity.” Journal of Convex Analysis 28 (2021), No. 3, 959–966. https://doi.org/10.68381/jca28056

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Published by Heldermann Verlag, 2021. Rights now held by Banach Press.