Traces of Sobolev functions on fractal type sets and characterization of extension domains

Journal of Functional Analysis

Volumn 143, Issue 1, 1997, Pages 221-246

  Hajłasz, Piotr ^a   Martio, Olli ^b  

^a UNIVERSITY OF WARSAW   (Poland)

^b UNIVERSITY OF HELSINKI   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030642447     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1996.2959     Document Type: Article

References (28)

1. 1. D. R. Adams, A trace inequality for generalized potentials, Studia Math. 48 (1973), 99-105.
2. 2. B. Bojarski, Remarks on Sobolev imbedding inequalities, in "Proc. of the Conference on Complex Analysis, Joensuu, 1987," Lecture Notes in Math., Vol. 1351, pp. 52-68, Springer-Verlag, Berlin/New York, 1988.
3. 3. H. Federer, "Geometric Measure Theory," Springer-Verlag, Berlin/New York, 1969.
4. 4. B. Franchi, G. Lu, and R. L. Wheeden, A relationship between Poincaré type inequalities and representation formulas in spaces of homogeneous type, preprint.
5. 5. E. Gagliardo, Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in n variabili, Rend. Sem. Mat. Univ. Padova 27 (1957), 284-305.
6. 6. D. Gilbarg and N. Trudinger, "Elliptic Partial Differential Equations of Second Order," Springer-Verlag, Berlin/New York, 1983.
7. 7. P. Hajłasz, Sobolev spaces on an arbitrary metric space, Potential Anal. 5 (1996), 403-415.
8. 8. P. Hajłasz, Boundary behaviour of Sobolev mappings, Proc. Amer. Math. Soc. 123 (1995), 1145-1148.
9. 9. P. Hajłasz, Geometric approach to Sobolev spaces and badly degenerated elliptic equations, Banach Center Publ., to appear.
10. 10. P. Hajłasz and P. Koskela, Isoperimetric inequalities and imbedding theorems in irregular domains, preprint.
11. 11. P. Hajłasz and P. Koskela, Sobolev meets Poincaré, C. R. Acad Sci. Paris 320 (1995), 1211-1215.
12. 12. P. Hajłasz and P. Koskela, Sobolev met Poincaré, in preparation.
13. 13. D. A. Herron and P. Koskela, Uniform, Sobolev extension and quasiconformal circle domains, J. Analyse Math. 57 (1991), 172-202.
14. 14. P. W. Jones, Quasiconformal mappings and extendability of functions in Sobolev spaces, Acta Math. 147 (1981), 71-88.
15. n, Trans. Amer. Math. Soc. 341 (1994), 355-370.
16. n," Harwood Academic, Reading, UK, 1984.
17. 17. J. Kinnunen and O. Martio, The Sobolev capacity on metric spaces, Ann. Acad. Sci. Fenn. Math. 21 (1996), 367-382.
18. 18. A. Kufner, O. John, and S. Fučik, "Function Spaces," Noordhoff, Leyden, 1977.
19. 19. G. J. Martin, Quasiconformal and bi-Lipschitz homeomorphisms, uniform domains and quasihyperbolic metric, Trans. Amer. Math. Soc. 292 (1985), 169-191.
20. 20. O. Martio, John domains, bilipschitz balls and Poincaré inequality, Rev. Roumaine Math. Pures Appl. 33 (1988), 107-112.
21. 21. O. Martio and J. Sarvas, Injectivity theorems in plane and space, Ann. Acad. Sci. Fenn. Ser. AI Math. 4 (1978/1979), 383-401.
22. 22. O. Martio and M. Vuorinen, Whitney cubes, p-capacity, and Minkowski content, Exposition. Math. 5 (1987), 17-40.
23. 23. V. G. Maz'ya, "Sobolev Spaces," Springer-Verlag, Berlin/New York, 1985.
24. 24. B. Øksendal, Null sets for measures orthogonal to R(X), Amer. J. Math. 94 (1972), 331-342.
25. 25. J. Peetre, A counterexample connected with Gagliardo's trace theorem, Comment. Math. Special Issue 2 (1979), 277-282.
26. 26. E. Stein, "Singular Integrals and Differentiability Properties of Functions," Princeton Univ. Press, Princeton, NJ, 1970.
27. 27. D. A. Trotsenko, Properties of regions with nonsmooth boundary, Sibirsk. Mat. Zh. 22 (1981), 221-224. [Russian]
28. 28. W. Ziemer, "Weakly Differentiate Functions," Graduate Texts in Mathematics, Vol. 120, Springer-Verlag, Berlin/New York, 1989.