Non-existence of solutions for some nonlinear elliptic equations involving measures

Royal Society of Edinburgh - Proceedings A

Volumn 130, Issue 1, 2000, Pages 167-187

  Orsina, L ^a   Prignet, A ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITÉ D'ORLÉANS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22844457175     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0308210500000093     Document Type: Article

References (27)

1. D. R. Adams and L. I. Hedberg. Function spaces and potential theory. Grundlehren der Matematischen Wissenschaften, vol. 314 (Springer, 1996).
2. P. Baras and M. Pierre. Singularités éliminables pour des équations semi-linéaires. Ann. Inst. Fourier (Grenoble) 34 (1984), 185-206.
3. N). Ann. Scuola Norm. Sup. Pisa Cl. Sci. 2 (1975), 523-555.
4. 1 theory of existence and uniqueness of nonlinear elliptic equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 22 (1995), 240-273.
5. L. Boccardo and T. Gallouët. Nonlinear elliptic and parabolic equations involving measure data. J. Funct. Analysis 87 (1989), 149-169.
6. L. Boccardo and T. Gallouët. Nonlinear elliptic equations with right-hand side measures. Comm. Partial Diff. Eqns 17 (1992), 641-655.
7. L. Boccardo and F. Murat. Increase of power leads to bilateral problems. In Composite media and homogenization theory (ed. G. Dal Maso and G. F. Dell'Antonio), pp. 113-123 (World Scientific, 1995).
8. L. Boccardo, T. Gallouët and L. Orsina. Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data. Ann. Inst. H. Poincaré Analysis Non Linéaire 13 (1996), 539-551.
9. L. Boccardo, T. Gallouët and L. Orsina. Existence and nonexistence of solutions for some nonlinear elliptic equations. J. Analysis Math. 73 (1997), 203-223.
10. N without growth restrictions on the data. J. Diff. Eqns 105 (1993), 334-363.
11. L. Boccardo, F. Murat and J. P. Puel. Existence of bounded solutions for nonlinear elliptic unilateral problems. Ann. Mat. Pura Appl. 152 (1988), 183-196.
12. H. Brezis. Nonlinear elliptic equations involving measures. In Contributions to nonlinear partial differential equations (Madrid, 1981), pp. 82-89. Research Notes in Mathematics, vol. 89 (Boston, MA: Pitman, 1983).
13. H. Brezis and L. Nirenberg. Removable singularities for nonlinear elliptic equations. Topol. Methods Nonlinear Analysis 9 (1997), 201-219.
14. 1. J. Math. Soc. Japan 25 (1973), 565-590.
15. F. E. Browder. Existence theorems for nonlinear partial differential equations (1970), In Global Analysis (Proc. Symp. Pure Math., Berkeley, CA, 1968), vol. XVI, pp. 1-60 (AMS, Providence, RI).
16. P. Dall'Aglio and C. Leone. Obstacles problems with measure data. Preprint SISSA-ISAS, Trieste, November 1997.
17. A. Dall'Aglio and L. Orsina. On the limit of some nonlinear elliptic equations involving increasing powers. Asympt. Analysis 14 (1997), 49-71.
18. G. Dal Maso, F. Murat, L. Orsina and A. Prignet. Definition and existence of renormalized solutions of elliptic equations with general measure data. C. R. Acad. Sci. Paris 325 (1997), 481-486.
19. G. Dal Maso, F. Murat, L. Orsina and A. Prignet. Renormalized solutions for elliptic equations with general measure data. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (In the press.)
20. M. Fukushima, K. Sato and S. Taniguchi. On the closable part of pre-Dirichlet forms and the fine supports of underlying measures. Osaka J. Math. 28 (1991), 517-535.
21. 1. Proc. R. Soc. Edinb. 96 (1984), 275-288.
22. J. Heinonen, T. Kilpeläinen and O. Martio. Nonlinear potential theory of degenerate elliptic equations (Oxford University Press, 1993).
23. J. Leray and J.-L. Lions. Quelques résultats de Višik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder. Bull. Soc. Math. France 93 (1965), 97-107.
24. J. L. Vazquez and L. Veron. Removable singularities of some strongly nonlinear elliptic equations. Manuscripta Math. 33 (1980/81), 129-144.
25. J. L. Vazquez and L. Veron. Isolated singularities of some semilinear elliptic equations. J. Diff. Eqns 60 (1985), 301-321.
26. L. Veron. Singularités éliminables d'équations elliptiques non linéaires. J. Diff. Eqns 41 (1981), 87-95.
27. W. Ziemer. Weakly differentiable functions, Sobolev spaces and functions of bounded variation. Graduate Texts in Mathematics (Springer, 1989).