Singular sets of Sobolev functions;Ensembles singuliers des fonctions de Sobolev

Comptes Rendus Mathematique

Volumn 334, Issue 7, 2002, Pages 539-544

  Žubrinić, Darko ^a  

^a UNIVERSITY OF ZAGREB   (Croatia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012204223     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1631-073X(02)02316-6     Document Type: Article

References (26)

1. D.R. Adams, L.I. Hedberg, Function Spaces and Potential Theory, Springer-Verlag, 1996.
2. N. Aronszajn, K.T. Smith, Theory of Bessel potentials I, Ann. Inst. Fourier (Grenoble) 13 (1956) 125-185.
3. T. Bagby, W. Ziemer, Pointwise differentiability and absolute continuity, Trans. Amer. Math. Soc. 194 (1974) 129-148.
4. A.P. Calderón, Lebesgue spaces of differentiable functions and distributions, in: Partial Differential Equations, Proc. Sympos. Pure Math., Vol. 4, American Mathematical Society, Providence, RI, 1961, pp. 33-49.
5. J. Deny, Les potentiels d'energie finie, Acta Math. 82 (1950) 107-183.
6. J. Deny, J.L. Lions, Les espaces du type de Beppo Levi, Ann. Inst. Fourier (Grenoble) 5 (1953-1954) 305-370.
7. K.J. Falconer, Fractal Geometry, Wiley, New York, 1990.
8. H. Federer, Geometric Measure Theory, Springer-Verlag, 1969.
9. B. Fuglede, Extremal length and functional completion, Acta Math. 98 (1957) 171-219.
10. B. Fuglede, On generalized potentials of functions in the Lebesgue classes, Math. Scand. 8 (1960) 287-304.
11. M. Grillot, Prescribed singular submanifolds of some quasilinear elliptic equations, Nonlinear Anal. 34 (1998) 839-856.
12. V.P. Havin, V.G. Mazya, Use of (p, l)-capacity in problems of the theory of exceptional sets, Mat. Sb. 90 (132) (1973) 558-591; Math. USSR-Sb. 19 (1973) 547-580.
13. J. Heinonen, T. Kilpeläinen, O. Martio, Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford University Press, Oxford, 1993.
14. S. Jaffard, Y. Meyer, Wavelet methods for pointwise regularity and local oscillations of functions, Mem. Amer. Math. Soc. 123 (587) (1996).
15. J. Keesling, Hausdorff dimension, Topology Proc. 11 (2) (1986) 349-383.
16. T. Kilpeläinen, Singular solutions to p-Laplacian type equations, Ark. Mat. 37 (1999) 275-289.
17. L. Korkut, M. Pašić, D. Žubrinić, Some qualitative properties of solutions of quasilinear elliptic equations and applications, J. Differential Equations 170 (2001) 247-280.
18. J. Malý, W.P. Ziemer, Fine Regularity of Solutions of Elliptic Partial Differential Equations, American Mathematical Society, 1997.
19. N.G. Meyers, Continuity properties of potentials, Duke Math. J. 42 (1975) 157-166.
20. L. Mou, Removability of singular sets of harmonic maps, Arch. Rational Mech. Anal. 127 (1994) 199-217.
21. Yu.G. Reshetnyak, On the concept of capacity in the theory of functions with generalized derivatives, Sibirsk. Mat. Zh. X (5) (1969) 1108-1138 (in Russian); Siberian Math. J. 13 (1969) 818-842.
22. J. Serrin, Isolated singularities of solutions of quasi-linear equations, Acta Math. 113 (1965) 219-240.
23. E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1970.
24. L. Veron, Singularities of Solutions of Second Order Quasilinear Equations, Addison-Wesley-Longman, 1996.
25. W.P. Ziemer, Weakly Differentiable Functions; Sobolev Spaces and Functions of Bounded Variation, Graduate Texts in Math., Springer-Verlag, 1989.
26. D. Žubrinić, Generating singularities of solutions of quasilinear elliptic equations, J. Math. Anal. Appl. 244 (2000) 10-16.