Quasiwypukłość i otwarte problemy analizy funkcjonalnej

• Autorzy: Kałamajska A.
• Języki publikacji: PL

Słowa kluczowe

PL

funkcja quasiwypukła; wypukłość rzędu jeden; hipoteza Morreya

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Wiadomości Matematyczne
• Rocznik: 2010
• Tom: T. 46, Nr 1
• Strony: 1--16
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Kałamajska A.

• Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego,

Bibliografia

• [1] J.-J. Alibert, B. Dacorogna, An example of a quasiconvex function that is not polyconvex in two dimensions, Arch. Rational Mech. Anal. 117 (1992), no. 2, 155-166.
• [2] K. Astala, Analytic aspects of quasiconformality, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), 1998, 617-626 (electronic).
• [3] J. M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1976/77), no. 4, 337-403.
• [4] J. M. Ball, Some open problems in elasticity, Geometry, mechanics, and dynamics, Springer, New York, 2002, 3-59.
• [5] K. Chełminski, A. Kałamajska, New convexity conditions in the calculus of variations and compensated compactness theory, ESAIM Control Optim. Calc. Var. 12 (2006), no. 1, 64-92.
• [6] L. C. Evans, Quasiconvexity and partial regularity in the calculus of variations, Arch. Rational Mech. Anal. 95 (1986), no. 3, 227-252.
• [7] T. Iwaniec, Nonlinear Cauchy-Riemann operators in Rn, Trans. Amer. Math. Soc. 354 (2002), no. 5, 1961-1995.
• [8] T. Iwaniec, C. Sbordone, Caccioppoli estimates and very weak solutions of elliptic equations, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 14 (2003), no. 3, 189-205 (2004). Renato Caccioppoli and modern analysis.
• [9] A. Kałamajska, On new geometric conditions for some weakly lower semicontinuous functionals with applications to the rank-one conjecture of Morrey, Proc. Roy. Soc. Edinburgh Sect. A 133 (2003), no. 6, 1361-1377.
• [10] D. Kinderlehrer, P. Pedregal, Gradient Young measures generated by sequences in Sobolev spaces, J. Geom. Anal. 4 (1994), no. 1, 59-90.
• [11] C. B. Morrey Jr., Quasi-convexity and the lower semicontinuity of multiple integrals, Pacific J. Math. 2 (1952), 25-53.
• [12] S. Müller, V. ˇSverák, Convex integration for Lipschitz mappings and counterexamples to regularity, Ann. of Math. 157 (2003), no. 3, 715-742.
• [13] V. ˇSverák, Rank-one convexity does not imply quasiconvexity, Proc. Roy. Soc. Edinburgh Sect. A 120 (1992), no. 1-2, 185-189.
• [14] L. Tartar, Compensated compactness and applications to partial differential equations, Nonlinear analysis and mechanics: Heriot-Watt Symposium, Vol. IV, Res. Notes in Math., vol. 39, Pitman, Boston, Mass., 1979, 136-212.