A quantitative Sobolev inequality in BV

Journal of Functional Analysis

Volumn 237, Issue 2, 2006, Pages 466-481

  Cianchi, Andrea ^a  

^a UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Functions of bounded variation; Isoperimetric inequalities; Lorentz spaces; Remainder terms; Sobolev inequalities

Indexed keywords

EID: 33646943552     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2005.12.008     Document Type: Article

References (24)

1. Alvino A., Ferone V., Lions P.L., and Trombetti G. Convex symmetrization and rearrangements. Ann. Inst. H. Poincaré, Anal. Non Linéaire 14 (1997) 275-293
2. Ambrosio L., Fusco N., and Pallara D. Functions of Bounded Variation and Free Discontinuity Problems (2000), Clarendon, Oxford
3. Aubin T. Problèmes isopérimetriques et espaces de Sobolev. J. Differential Geom. 11 (1976) 573-598
4. Bartsch T., Weth T., and Willem M. A Sobolev inequality with remainder term and critical equations on domains with topology for the polyharmonic operator. Calc. Var. Partial Differential Equations 18 (2003) 57-75
5. Bianchi G., and Egnell H. A note on the Sobolev inequality. J. Funct. Anal. 100 (1991) 18-24
6. Brezis H., and Lieb E. Sobolev inequalities with remainder terms. J. Funct. Anal. 62 (1985) 73-86
7. Brezis H., and Nirenberg L. Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Comm. Pure Appl. Math. 36 (1983) 437-477
8. Cordero-Erausquin D., Nazaret B., and Villani C. A mass transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities. Adv. Math. 182 (2004) 307-332
9. De Giorgi E. Sulla proprietà isoperimetrica dell'ipersfera, nella classe degli insiemi aventi frontiera orientata di misura finita. Atti. Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Nat. Sez. I (8) 5 (1958) 33-44
10. Esposito L., Fusco N., and Trombetti C. A quantitative version of the isoperimetric inequality: the anisotropic case. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) IV (2005) 1-33
11. Evans L.C., and Gariepy R.F. Measure Theory and Fine Properties of Functions (1992), CRC Press, Boca Raton, FL
12. Federer H., and Fleming W. Normal and integral currents. Ann. of Math. 72 (1960) 458-520
13. Fleming W., and Rischel R. An integral formula for total gradient variation. Arch. Math. 11 (1960) 218-232
14. Fonseca I., and Müller S. A uniqueness proof for the Wulff theorem. Proc. Roy. Soc. Edinburgh Sect. A 119 (1991) 125-136
15. Fusco N. The classical isoperimetric theorem. Rend. Accad. Sci. Fis. Mat. Napoli (4) 71 (2004) 63-107
16. Gazzola F., Grunau H.C., and Squassina M. Existence and nonexistence results for critical growth biharmonic elliptic equations. Calc. Var. Partial Differential Equations 18 (2003) 117-143
17. Hall R.R. A quantitative isoperimetric inequality in n-dimensional space. J. Reine Angew. Math. 428 (1992) 161-196
18. Maz'ya V.M. Classes of regions and imbedding theorems for function spaces. Dokl. Akad. Nauk. SSSR 133 (1960) 527-530 (in Russian). English translation:
19. Maz'ya V.M. Classes of regions and imbedding theorems for function spaces. Soviet Math. Dokl. 1 (1960) 882-885
20. Maz'ya V.M. Sobolev Spaces (1985), Springer-Verlag, Berlin
21. Talenti G. Best constant in Sobolev inequality. Ann. Mat. Pura Appl. 110 (1976) 353-372
22. Talenti G. The standard isoperimetric theorem. In: Gruber P.M., and Wills J.M. (Eds). Handbook of Convex Geometry (1993), North-Holland, Amsterdam
23. Taylor J. Existence and structure of solutions to a class of nonelliptic variational problems. Sympos. Math. 14 (1974) 499-508
24. Ziemer W.P. Weakly Differentiable Functions (1989), Springer-Verlag, New York