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Journal of Convex Analysis 28 (2021), No. 3, [final page numbers not yet available]
Copyright Heldermann Verlag 2021



Field Theory for Integrands with Low Regularity

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



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.

Keywords: Integral functionals, obstacle problems, singular ellipticity, Tonelli regularity, existence and regularity in small, field theory.

MSC: 49N60.

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