A remark on comparison results for first-order Hamilton-Jacobi equations

Nonlinear Analysis, Theory, Methods and Applications

Volumn 28, Issue 9, 1997, Pages 1465-1477

  Mercaldo, A ^a  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

Hamilton Jacobi equations; Optimization; Rearrangements

Indexed keywords

FUNCTIONS; NONLINEAR EQUATIONS; OPTIMIZATION; THEOREM PROVING;

HAMILTON-JACOBI EQUATION; HARDY INEQUALITY; STEEPEST DESCENT METHOD;

INTEGRAL EQUATIONS;

EID: 0031142299     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(96)00011-9     Document Type: Article

References (25)

1. BANDLE C., Isoperimetric Inequalities and Applications. Monographs and Studies in Mathematics, No. 7, Pitman, London (1980).
2. CHONG K. M. & RICE N. M., Equimeasurable Rearrangements of Functions. Queen's papers in pure and applied mathematics, No. 28. Queen's University, Ontario (1971).
3. HARDY G. H., LITTLEWOOD J. E. & POLYA G., Inequalities. Cambridge University Press, Cambridge (1964).
4. KAWOHL B., Rearrangements and Convexity of Level Sets in P.D.E. Lecture Notes in Mathematics, No. 1150. Springer, Berlin (1985).
5. MOSSINO J., Inégalités Isopérimetriques et Applications en Physique. Collection Travaux en Cours, Hermann, Paris (1984).
6. CRANDALL M. G., EVANS L. C. & LIONS P. L., Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Am. math. Soc. 282, 487-502 (1984).
7. CRANDALL M. G. & LIONS P. L., Viscosity solutions of Hamilton-Jacobi equations, Trans. Am. math. Soc. 277, 1-42 (1983).
8. LIONS P. L., Generalized Solutions of Hamilton-Jacobi Equations. Pitman Lecture Notes, London (1982).
9. ARONSSON G. & TALENTI G., Estimating the integral of a function in terms of a distribution function of its gradient, Boll. U.M.I. B 18, 885-894 (1981).
10. ALVINO A., LIONS P. L. & TROMBETTI G., A remark on comparison results via symmetrization, Proc. R. Soc. Edinb. 102A, 37-48 (1986).
11. GIARRUSSO E., Estimate for generalized subsolution of first-order Hamilton-Jacobi equations and rearrangements, Nonlinear Analysis 18, 9-16 (1992).
12. GIARRUSSO E. & NUNZIANTE D., Symmetrization in a class of first-order Hamilton-Jacobi equations, Nonlinear Analysis 8, 289-299 (1984).
13. GIARRUSSO E. & NUNZIANTE D., Comparison theorem for a class of first-order Hamilton-Jacobi equations, Ann. Fac. Sci. Toulouse Math. 7, 57-73 (1985).
14. BETTA M. F. & MERCALDO A., Uniqueness results for optimization problems with prescribed rearrangement, Potential Anal. 5, 183-205 (1996).
15. MERCALDO A., Simmetrizzazione sferica, risultati di confronto e condizioni di ottimalità. Tesi di dottorato, Université di Napoli (1995).
16. KESAVAN S., Some remarks on a result of Talenti, Annali Scu. norm. sup. Pisa 15, 453-465 (1988).
17. KESAVAN S., On a Comparison Theorem via Symmetrization. Proc. R. Soc. Edinb. 119A, 159-167 (1991).
18. FERONE V. & POSTERARO M. R., A remark on a comparison theorem, Communs partial diff. Eqns 16, 1255-1262 (1991).
19. ALVINO A. & TROMBETTI G., Sulle migliori constanti di maggiorazione per una classe di equazioni ellittiche degeneri, Ricerche di Mat. 27, 413-428 (1978).
20. ALVINO A., LIONS P. L. & TROMBETTI G., On optimization problems with prescribed rearrangements. Nonlinear Analysis 13, 185-220 (1989).
21. BURTON G. R., Rearrangements of functions, maximization of convex functionals, and vortex rings, Math. Ann 216, 225-253 (1987).
22. TALENTI G., Elliptic equations and rearrangements, Annali Scu. norm. sup. Pisa 3, 697-718 (1976).
23. DE GIORGI E., Su una teoria generale della misura (r - 1)-dimensionale in uno spazio ad r dimensioni, Annali Mat. pura appl. 36, 191-213 (1954).
24. FLEMING W. & RISHEL R., An integral formula for total gradient variation, Arch. Math. 11, 218-222 (1960).
25. BROTHERS J. E. & ZIEMER W. P., Minimal rearrangements of Sobolev function, J. reine angew. Math. 384, 153-179 (1988).