References
- R. A. Adams, Sobolev Spaces, Academic press, New York, 1975.
- L. Ambrosio, N. Gigli, and G. Savare, Gradient flows, Gradient flows in metric spaces and in the space of probability measures, Lectures in Mathematics ETH Zurich. Birkhauser Verlag, Basel, 2005.
- J. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1976/77), no. 4, 337–403. https://doi.org/10.1007/BF00279992
- J. Ball and V. J. Mizel, One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation, Arch. Rational Mech. Anal. 90 (1985), no. 4, 325–388. https://doi.org/10.1007/BF00276295
- H. Berliocchi and J.-M. Lasry, Int´egrandes normales et mesures param´etr´ees en calcul des variations, Bull. Soc. Math. France 101 (1973), 129–184.
- P. Bernard and B. Buffoni, Optimal mass transportation and Mather theory, J. Eur. Math. Soc. (JEMS) 9 (2007), no. 1, 85–121.
- P. Bernard, Young measures, superposition and transport, Indiana Univ. Math. J. 57 (2008), no. 1, 247–275. https://doi.org/10.1512/iumj.2008.57.3163
- Y. Brenier, Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations, Comm. Pure Appl. Math. 52 (1999), no. 4, 411–452. https://doi.org/10.1002/(SICI)1097-0312(199904)52:4<411::AID-CPA1>3.0.CO;2-3
- G. Buttazzo, Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations, Pitman Research Notes in Mathematics Series, 207. Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1989.
- B. Dacorogna, Direct methods in the calculus of variations, Second edition. Applied Mathematical Sciences, 78. Springer, New York, 2008.
- L. C. Evans and R. F. Gariepy, Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics. CRC Press, Boca Raton, FL, 1992.
- M. Giaquinta, G. Modica, and J. Soucek, Cartesian Currents in the Calculus of Variations I, Springer, Berlin, 1998.
- M. Giaquinta, G. Modica, and J. Soucek, Cartesian Currents in the Calculus of Variations II, Springer, Berlin, 1998.
- P. Pedregal, Parametrized Measures and Variational Principles, Progress in Nonlinear Differential Equations and their Applications, 30. Birkh auser Verlag, Basel, 1997.
- M. Valadier, A course on Young measures, Rend. Istit. Mat. Univ. Trieste 24 (1994), 349–394.
- C. Villani, Topics in Optimal Transportation, Graduate Studies in Mathematics, 58. American Mathematical Society, Providence, RI, 2003.
- L. C. Young, Lectures on the Calculus of Variations and Optimal Control Theory, Second edition, Chelsea, 1980.