Journal of Convex Analysis 28 (2021), No. 3, 959--966
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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