Richard Gratwick
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
Richard Gratwick
r.gratwick@ed.ac.ukMikhail A. Sychev
masychev@math.nsc.ruReferences
- G. Buttazzo, M. Giaquinta, S. Hildebrandt: One-dimensional Variational Problems. An Introduction, Oxford University Press, Oxford (1998).https://doi.org/10.1093/oso/9780198504658.001.0001Google Scholar
- R. Gratwick, M. A. Sychev: One-dimensional variational obstacle problems, Pure Appl. Funct. Analysis 4/3 (2019) 547–558.Google Scholar
- R. Gratwick, M. A. Sychev: Direct methods in variational field theory, Sib. Math. J., submitted.Google Scholar
- M. A. Sychev: On the question of regularity of the solutions of variational problems, Russian Acad. Sci. Sb. Math. 75/2 (1993) 535–556.https://doi.org/10.1070/SM1993v075n02ABEH003397Google Scholar
- M. A. Sychev: Another theorem of classical solvability ‘in small’ for one-dimensional variational problems, Arch. Ration. Mech. Analysis 202/1 (2011) 269–294.https://doi.org/10.1007/s00205-011-0416-0Google Scholar
- M. A. Sychev: Variational field theory from the point of view of direct methods, Sib. Math. J. 58/5 (2017) 891–898.https://doi.org/10.1134/S0037446617050160Google Scholar
- L. Tonelli: Sur une méthode directe du calcul des variations, Rend. Circ. Mat. Palermo 39 (1915) 233–264.https://doi.org/10.1007/BF03015981Google Scholar
Suggested citation
Published by Heldermann Verlag, 2021. Rights now held by Banach Press LLC.
