On the regularity of solutions of one-dimensional variational obstacle problems

References

[1] G. Buttazzo, M. Giaquinta and S. Hildebrandt, One-Dimensional Variational Problems. An introduction, Oxford Lecture Ser. Math. Appl. 15, Clarendon Press, Oxford, 1998. 10.1093/oso/9780198504658.001.0001Search in Google Scholar

[2] R. Gratwick and D. Preiss, A one-dimensional variational problem with continuous Lagrangian and singular minimizer, Arch. Ration. Mech. Anal. 202 (2011), no. 1, 177–211. 10.1007/s00205-011-0413-3Search in Google Scholar

[3] R. Gratwick, M. A. Sychev and A. S. Tersenov, Regularity and singularity phenomena for one-dimensional variational problems with singular ellipticity, Pure Appl. Funct. Anal. 1 (2016), no. 3, 397–416. Search in Google Scholar

[4] Y. G. Reshetnyak, Stability Theorems in Geometry and Analysis, Math. Appl. 304, Kluwer Academic, Dordrecht, 1994. 10.1007/978-94-015-8360-2Search in Google Scholar

[5] M. A. Sychev, On the regularity of solutions of a one-dimensional variational problem, Proceedings of the XXVII All-Union Scientific Student Conference “The Student and Scientific-Technological Progress” (Novosibirsk 1989), Novosibirskij Gosudarstvennyj Universitet, Novosibirsk (1989), 60–65. Search in Google Scholar

[6] M. A. Sychev, Regularity of solutions of some variational problems, Dokl. Akad. Nauk SSSR 316 (1991), no. 6, 1326–1330. Search in Google Scholar

[7] M. A. Sychev, On the regularity of solutions of variational problems, Mat. Sb. 183 (1992), no. 4, 118–142. Search in Google Scholar

[8] M. A. Sychev, Another theorem of classical solvability ‘in small’ for one-dimensional variational problems, Arch. Ration. Mech. Anal. 202 (2011), no. 1, 269–294. 10.1007/s00205-011-0416-0Search in Google Scholar