Variations, approximation, and low regularity in one dimension

Richard Gratwick1
1School of Mathematics, Edinburgh, UK

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Tài liệu tham khảo

Ball, J.M.: Singularities and computation of minimizers for variational problems. In: Foundations of Computational Mathematics (Oxford, 1999), London Mathematical Society Lecture Note Series, vol. 284, pp. 1–20. Cambridge University Press, Cambridge (2001)

Ball, J.M., Mizel, V.J.: One-dimensional variational problems whose minimizers do not satisfy the Euler–Lagrange equation. Arch. Ration. Mech. Anal. 90(4), 325–388 (1985)

Buttazzo, G., Giaquinta, M., Hildebrandt, S.: One-dimensional variational problems. An introduction, Oxford Lecture Series in Mathematics and its Applications, vol. 15. The Clarendon Press Oxford University Press, New York (1998)

Clarke, F.H., Vinter, R.B.: Regularity properties of solutions to the basic problem in the calculus of variations. Trans. Am. Math. Soc. 289(1), 73–98 (1985)

Csörnyei, M., Kirchheim, B., O’Neil, T.C., Preiss, D., Winter, S.: Universal singular sets in the calculus of variations. Arch. Ration. Mech. Anal. 190(3), 371–424 (2008)

Esposito, L., Leonetti, F., Mingione, G.: Sharp regularity for functionals with $$(p, q)$$ ( p , q ) growth. J. Differ. Equ. 204(1), 5–55 (2004)

Evans, L., Gariepy, R.: Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics. CRC Press, Boca Raton (1992)

Ferriero, A.: A direct proof of the Tonelli’s partial regularity result. Discrete Contin. Dyn. Syst. 32(6), 2089–2099 (2012)

Ferriero, A.: On the Tonelli’s partial regularity. Differ. Integral Equ. 26(1–2), 1–9 (2013)

Gratwick, R.: Singular minimizers in the calculus of variations. Ph.D. thesis, University of Warwick (2011)

Gratwick, R., Preiss, D.: A one-dimensional variational problem with continuous Lagrangian and singular minimizer. Arch. Ration. Mech. Anal. 202(1), 177–211 (2011)

Lavrentiev, M.: Sur quelques problèmes du calcul des variations. Ann. Mat. Pura Appl. 4, 7–28 (1926)

Manià, B.: Sopra un essempio di Lavrentieff. Bull. Un. Mat Ital. 13, 147–153 (1934)

Sychëv, M.A.: On the regularity of solutions of variational problems. Russ. Acad. Sci. Sb. Math. 75(2), 535–556 (1993)

Tonelli, L.: Fondamentica di Calcolo delle variazioni, vol. 2. Zanichelli, Bologna (1923)

Tonelli, L.: Su gli integrali del calcolo delle variazioni in forma ordinaria. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (2) 3(3–4), 401–450 (1934)