Tính Quy Tắc Toàn Cục cho Các Bài Tối Ưu của Một Số Tổ Hợp Biến Thiên

De Giorgi, E.: Un esempio di estremali discontinue per un problema variazionale ditipo ellittico. [An example of discontinuous extremals for an elliptic type variational problem]. Boll. Un. Mat. Ital. 4, 135–137 (1968) Mingione, G.: Regularity of minima: an invitation to the dark side of the calculus of variations. Arch. Rational Mech. Anal. 51, 355–426 (2006) Carozza, M., Passarelli, A.: Model problems from nonlinear elasticity: partial regularity results. ESAIM Control Opt. Calc. Var. 13, 120–134 (2007) Fuchs, M., Seregin, G.: Partial regularity of the deformation gradient for some model problems in nonlinear twodimensional elasticity. Algebra Anal. 6, 128–153 (1994) Fusco, N., Hutchinson, J.E.: Partial regularity in problem motivated by nonlinear elasticity. SIAM J. Math. Anal. 22, 1516–1551 (1991) Fuchs, M., Reuling, G.: Partial regularity for certain classes of polyconvex functionals related to non linear elasticity. Manuscr. Math. 87, 13–26 (1995) Fusco, N., Hutchinson, J.E.: Partial regularity and everywhere continuity for a model problem from non-linear elasticity. J. Austral. Math. Soc. Ser. A 57, 158–169 (1994) Cupini, G., Leonetti, F., Mascolo, E.: Local boundedness for mininizers of some polyconvex integrals. Arch. Rat. Mech. Anal. 224, 269–289 (2017) Leonetti, F.: Pointwise estimates for a model problem in nonlinear elasticity. In: Forum Math. vol. 18, pp. 529–534 (2006) D’Ottavio, A., Leonetti, F., Musciano, C.: Maximum principle for vector-valued mappings minimizing variational integrals. Atti. Sem. Mat. Fis. Modena 46, 677–683 (1998) Leonetti, F., Siepe, F.: Maximum principle for vector-valued minimizers of some intergral functionals. J. Convex Anal. 12, 267–278 (2005) Leonetti, F., Siepe, F.: Bounds for vector valued minimizers of some integral functionals. Ricerche Mat. 54, 303–312 (2005) Gao, H., Leonetti, F., Macri, M., Petricca, P.V.: Regularity for minimizers with positive Jacobian. Appl. Anal. 39, 496–507 (2020) Ball, J.M.: Convexity conditions and existence theorems in nonlinear elasticity. Arch. Ration. Mech. Anal. 63, 337–403 (1977) Ball J.M.: Constitutive inequalities and existence thorems in elastostatics. In: Nonlinear Analysis and Mechanics, Proceedings, Research Notes Pitman, London, vol. 17, pp. 13–25 (1977) Bauman, P., Owen, N., Phillps, D.: Maximum principles and a priori estimates for a class of problems from nonlinear elasticity. Ann. Inst. Henri Poincaré Anal. Nonlineaire 8, 119–157 (1991) Müller, S.: Higher integrability of determinats and weak convergence in \(L^1\). J. Reine Angew. Math. 412, 20–34 (1990) Dacorogna B.: Direct methods in the calculus of variations. In: Applied Mathematical Sciences, vol. 78, 2nd edn, Springer, New York (2008) Carozza, M., Gao, H., Giova, R., Leonetti, F.: Local boundedness for minimizers of some polyconvex integrals. J. Optim. Theory Appl. 178, 699–725 (2018) Morrey, C.B.: Multiple Integrals in the Calculus of Variations. Springer, Berlin (1966) Giaquinta, M.: Growth condition and regularity, a counterexample. Manuscr. Math. 59, 245–248 (1987) Esposito, L., Leonetti, F., Mingione, G.: Sharp regularity results for functionals with \((p, q)\) growth. J. Differ. Equ. 204, 5–55 (2004) Hong, M.C.: Some remarks on the minimizers of variational integrals with non standard growth conditions. Boll. Un Mat. Ital. A6, 91–101 (1992) Marcellini, P.: Regularity of minimizers of integrals of the calculus of variations with non standard growth conditions. Arch. Rational Mech. Anal. 105, 267–284 (1989) Marcellini, P.: Regularity and existence of solutions of elliptic equations with \(p-q\)-growth conditions. J. Differ. Equ. 90, 1–30 (1991) Acerbi, E., Fusco, N.: Partial regularity under anisotropic \((p, q)\) growth conditions. J. Differential Equations 107, 46–67 (1994) Moscariello, G., Nania, L.: Hölder continuity of minimizers of functionals with non standard growth conditions. Ricerche Mat. 40, 259–273 (1991) Marcellini, P.: Growth conditions and regularity for weak solutions to nonlinear elliptic pdes. J. Math. Anal. Appl. (2020). https://doi.org/10.1016/j.jmaa.2020.124408 Tang, Q.: Regularity of minimizers of non-isotropic integrals of the calculus of variations. Ann. Mat. Pura Appl. 164, 77–87 (1993) Lions, J.L.: Quelques methodes de resolution des problemes aux limites non lineaires [Some methods of solving non-linear boundary problems]. Dunod-Gauthier-Villars, Paris (1969) Fusco, N., Sbordone, C.: Some remarks on the regularity of minima of anisotropic integrals. Commun. Partial Differ. Equ. 18, 153–167 (1993) Leonetti, F., Siepe, F.: Global integrability for minimizers of anisotropic functionals. Manuscr. Math. 144, 91–98 (2014) Boccado L., Croce G.: Elliptic Partial Differential Equations. De Gruyter Studies in Mathematics vol 55, De Gruyter, Berlin (2014) Stein, E., Weiss, G.: Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press, Princeton (1971) Troisi, M.: Teoremi di inclusione per spazi di Sobolev non isotropi. [Inclusion theorems for anisotropic Sobolev spaces]. Ricerche Mat. 18, 3–24 (1969) Stampacchia G.: Équations elliptiques du second ordre à coefficients discontinus [Second order elliptic equations with discontinuous coefficients] Séminaire Jean Leray, 1963–1964 (3), 1–77 (1963) Gao, H., Leonetti, F., Wang, L.: Remarks on Stampacchia lemma. J. Math. Anal. Appl. 458, 112–122 (2018) Gao, H., Di, Q., Ma, D.: Integrability for solutions to some anisotropic obstacle problems. Manuscr. Math. 146, 433–444 (2015) Innamorati, A., Leonetti, F.: Global integrability for weak solutoins to some anisotropic elliptic equations. Nonlinear Anal. 113, 430–434 (2015) Kovalevsky, A.A.: Integrability and boundedness of solutions to some anisotropic problems. J. Math. Anal. Appl. 432, 820–843 (2015) Leonetti, F., Petricca, P.V.: Global summability for solutoins to some anisotropic elliptic systems. Adv. Differ. Equ. 20, 1165–1186 (2015) Kovalevskii, A.A.: On the summability of entropy solutions for the Dirichlet problem in a class of non-linear elliptic fourth-order equations. Izvestiya Math. 67, 881–894 (2003)