Mascolo, Elvira; Schianchi, Rosanna Existence theorems for non convex problems. (English) Zbl 0522.49001 J. Math. Pures Appl., IX. Sér. 62, 349-359 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 16 Documents MSC: 49J10 Existence theories for free problems in two or more independent variables 49J20 Existence theories for optimal control problems involving partial differential equations 49J45 Methods involving semicontinuity and convergence; relaxation 26B35 Special properties of functions of several variables, Hölder conditions, etc. 74B20 Nonlinear elasticity Keywords:multiple integrals; existence of minima; non convex problems PDFBibTeX XMLCite \textit{E. Mascolo} and \textit{R. Schianchi}, J. Math. Pures Appl. (9) 62, 349--359 (1983; Zbl 0522.49001) References: [1] Aubert, G.; Tahraoui, R.: Théorèmes d’existence en optimisation non convexe. Appl. anal. 18, 75-100 (1984) · Zbl 0522.49002 [2] Crandall, M. G.; Lions, P. L.: Viscosity solutions of Hamilton-Jacobi equations. Trans. amer. Math. soc. 277, 1-42 (1983) · Zbl 0599.35024 [3] Giaquinta, M.; Modica, G.: Regolarità lipschitziana per la soluzione di alcuni problemi di minimo con vincolo. Ann. mat. Pura appl. 106, 85-117 (1975) · Zbl 0325.49009 [4] Giaquinta, M.; Giusti, E.: On the regularity of the minima of variational integrals. Acta math. 148 (1982) · Zbl 0494.49031 [5] Giusti, E.: Equazioni ellittiche del secondo ordine. (1978) · Zbl 1308.35001 [6] Hartman, P.; Stampacchia, G.: On some non linear elliptic differential-functional equations. Acta math. 115, 383-421 (1966) · Zbl 0142.38102 [7] D. Kinderleherer and E. Mascolo, Local minima for non convex problems, preprint. [8] Kinderleherer, D.; Stampacchia, G.: An introduction to variational inequalities and their applications. (1980) [9] Ladyzhenskaya, O.; Ural’tseva, N.: Linear and quasilinear elliptic equations. (1968) · Zbl 0164.13002 [10] Marcellini, P.: Alcune osservazioni sull’esistenza del minimo di integrali del calcolo delle variazioni senza ipotesi di convessità. Rend. mat. 13 (1980) · Zbl 0454.49015 [11] Marcellini, P.: A relation between existence of minima for non convex integrals and uniqueness for non strictly convex integrals of the calculus of variations. Lecture notes in math. (1982) [12] Marcellini, P.: Some remarks on uniqueness in the calculus of variations. Nonlinear PDE and their applications, college de France seminar (1983) · Zbl 0521.49005 [13] Marcellini, P.; Sbordone, C.: Semicontinuity problems in the calculus of variations. Nonlinear anal. 4, 241-257 (1980) · Zbl 0537.49002 [14] Mascolo, E.; Schianchi, R.: Existence theorems for non convex problems. J. math. Pures appl. 62, 349-359 (1983) · Zbl 0545.49002 [15] Mascolo, E.; Schianchi, R.: Un theorem d’existence pour des problems du calcul des variations non convexes. C. R. Acad. sci. Paris 297, 615-617 (1983) · Zbl 0545.49002 [16] Mascolo, E.; Schianchi, R.: Non convex problems of the calculus of variations. Nonlinear anal. 9, 371-379 (1985) [17] Serrin, J.: The problem of Dirichlet for quasilinear elliptic differential with many independent variables. Philos. trans. Roy. soc. London ser. A 264, 413-490 (1969) · Zbl 0181.38003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.