Existence and Regularity of Minimizers of Nonconvex Functionals Depending onuand ∇u

Journal of Mathematical Analysis and Applications

Volumn 230, Issue 1, 1999, Pages 30-56

  Celada, Pietro ^a  

^a UNIVERSITY OF TRIESTE   (Italy)

Author keywords

Existence and regularity of solutions; Nonconvex minimum problems

Indexed keywords

EID: 0042044425     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1998.6163     Document Type: Article

References (20)

1. Celada P., Cellina A. Existence and nonexistence of solutions to a variational problem on a square. Houston J. Math. 24:1998;345-375.
2. Celada P., Perrotta S., Treu G. Existence of solution for a class of non convex minimum problems. Math. Z. 228:1998;177-199.
3. Cellina A. On minima of a functional of the gradient: necessary conditions. Nonlinear Anal. 20:1993;337-341.
4. Cellina A. On minima of a functional of the gradient: sufficient conditions. Nonlinear Anal. 20:1993;343-347.
5. Cellina A. Minimizing a functional depending on ∇uu. Ann. Inst. H. Poincaré Anal. Non Linéaire. 14:1997;339-352.
6. Cellina A., Perotta S. On minima of radially symmetric functionals of the gradient. Nonlinear Anal. 23:1994;239-249.
7. G. Crasta, On the minimum problem for a class of non coercive, non convex functionals, SIAM J. Control Optim.
8. G. Crasta, Existence, uniqueness and qualitative properties of minima to radially symmetric, noncoercive, nonconvex variational problems, 1998.
9. F. S. De Blasi, G. Pianigiani, On the Dirichlet problem for Hamilton-Jacobi equations. A Baire category approach, 1997.
10. Ekeland I., Temam R. Convex Analysis and Variational Problems. 1976;North-Holland, Amsterdam.
11. Goodman J., Kohn R. V., Reyna L. Numerical study of a relaxed variational problem from optimal design. Comput. Methods Appl. Mech. Engrg. 57:1986;107-127.
12. Kawhol B., Stara J., Wittum G. Analysis and numerical studies of a problem of shape design. Arch. Rational Mech. Anal. 114:1991;349-363.
13. Ladyzhenskaya O. A., Ural'tseva N. N. Linear and quasilinear elliptic equations. Mathematics in Science and Engineering. 1968;Academic Press, New York.
14. Mascolo E., Schianchi R. Existence theorems in the calculus of variations. J. Differential Equation. 67:1987;185-198.
15. Murat F., Tartar L. Calcul des variations et homogenization. Bergman D. Les methodes de l'homogenization: théorie et applications en physique. 1985.
16. Rockafeller T. Convex Analysis. 1972;Princeton Univ. Press, Princeton.
17. M. A. Sychev, Characterization of Homogeneous Scalar Variational Problems Solvable for all Boundary Data, 97-203, Carnegie Mellon University, 1997.
18. G. Treu, An existence result for a class of nonconvex problems of the calculus of variations, J. Convex Anal.
19. N. Proc. Roy. Soc. Edinburgh Sect. A. 127:1997;1089-1101.
20. S. Zagatti, Minimization of functionals of the gradient by Baire's theorem.