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Two-dimensional stable Lavrentiev phenomenon with and without boundary conditions

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This work contains examples of regular 2D problems of the Calculus of Variations which exhibit stable Lavrentiev phenomenon, under different types of boundary conditions.
Rocznik
Strony
689--707
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
  • Departamento de Matematica Universidade de Aveiro, Portugal
autor
  • DiMaD, Universita di Firenze, Italia
autor
  • Escola Superior de Tecnologia e Gestao de Agueda Universidade de Aveiro, Portugal
Bibliografia
  • Alberti, G. and Majer, P. (1994) Gap phenomenon for some autonomous functionals. J. Convex Anal. 1, 31-45.
  • Ball, J.M. and Mizel, V.J. (1985) One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equations. Arch. Rational Mech. Anal. 90, 325-338.
  • Buttazzo, G. and Belloni, M. (1995) A survey on old and recent results about the gap phenomenon in the calculus of variations. Recent Developments in Well-Posed Variational Problems. Kluwer Acad. Publ., 1-27.
  • Clarke, F.H. and Vinter, R.B. (1985) Regularity properties of solutions to the basic problem in the calculus of variations. Trans. Amer. Math. Soc. 289, 73-98.
  • Dacorogna, B. (1989) Direct Methods in the Calculus of Variations. Berlin-Heidelberg-New York-London-Paris-Tokyo, Springer-Verlag.
  • Dani, K., Hrusa, W.J. and Mizel, V.J. (2000) Lavrentiev phenomenon for totally unconstrained variational problems in one dimension. NoDEA Nonlinear Differential Equations Appl. 7, 435-446.
  • Evans, L.C. and Gariepy, R.F. (1992) Measure Theory and Fine Properties of Functions. CRC Press.
  • Foss, M. (2003) Examples of the Lavrentiev phenomenon with continuous Sobolev exponent dependence. J. Convex Anal. 10, 445-464.
  • Foss, M., Hrusa, W.J. and Mizel, V.J. (2003) The Lavrentiev gap phenomenon in nonlinear elasticity. Arch. Rational Mech. Anal. 167, 337-365.
  • Horst, R., Pardalos, P.M. and Thoai, N.V. (2000) Introduction to Global Optimization. Kluwer Academic Publishers.
  • Lavrentiev, M. (1927) Sur quelques problemes du calcul des variations. Ann. Mat. Pura Appl. 4, 7-28.
  • Loewen, P.D. (1987) On the Lavrentiev phenomenon. Canadian Math. Bulletin 30, 102-108.
  • Mania, B. (1934) Sopra un esempio di Lavrentieff. Boll. Un. Mat. Ital. 13, 146-153.
  • Ornelas, A. (2004) Lipschitz Regularity for ScalarMinimizers of Autonomous Simple Integrals. J. Math. Anal. Appl. 300, 285-296.
  • Sarychev, A.V. (1985) First and Second-Order integral functionals of the calculus of variations which exhibit the Lavrentiev phenomenon. J. Dynam. Control Systems 3, 565-588.
  • Torres, D.F.M. (2003) Lipschitzian Regularity of the Minimizing Trajectories for Nonlinear Optimal Control Problems. Math. Control Signals Systems 16, 158-174.
  • Zhikov, V.V. (1995) On Lavrentiev’s phenomenon. Russian J. Math. Phys. 3, 249-269.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0008-0009
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