On the solvability of the equation div u = f in L1 and in C 0

Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni

Volumn 14, Issue 3, 2003, Pages 239-245

  Dacorogna, Bernard ^a   Fusco, Nicola ^b   Tartar, Luc ^c  

^a EPFL   (Switzerland)

^b UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^c CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Divergence; Lorentz spaces; Sobolev imbedding theorem

Indexed keywords

EID: 84887232209     PISSN: 11206330     EISSN: 17200768     Source Type: Journal    
DOI: None     Document Type: Article

References (9)

1. J. BERGH - J. LÖFSTRÖ, Interpolation spaces: an introduction. Springer-Verlag, Berlin 1976.
2. J. BOURGAIN - H. BREZIS, Sur l'équation div u4f. C. R. Acad. Sci. Paris, ser. I, 334, 2002, 973-976.
3. D. GILBARG - N.S. TRUDINGER, Elliptic partial differential equations of second order. Springer-Verlag, Berlin 1977.
4. C.T. MC MULLEN, Lipschitz maps and nets in Euclidean space. Geom. Funct. Anal., 8, 1998, 304-314.
5. 1 norm. Arch. Ration. Mech. Anal., 11, 1962, 40-49.
6. D. PREISS, Additional regularity for Lipschitz solutions of PDE. J. Reine Angew. Math., 485, 1997, 197-207.
7. E.M. STEIN, Singular integrals and differentiability properties of functions. Princeton University Press, Princeton 1970.
8. E.M. STEIN - G. WEISS, Introduction to Fourier analysis on Euclidean spaces. Princeton University Press, Princeton 1971.
9. L. TARTAR, Imbedding theorems of Sobolev spaces into Lorentz spaces. Bollettino UMI, 1-B, 1998, 479-500. (Pubitemid 128443267)