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
School of Mathematics, The University of Edinburgh, United Kingdom
Mikhail A. Sychev
Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russia
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.
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