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Elliptic equations and maps of bounded length distortion

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References

  1. Federer, H.: Geometric measure theory. Berlin, Heidelberg, New York: Springer 1969

    Google Scholar 

  2. Gehring, F.W., Martio, O.: Quasiextremal distance domains and extension of quasiconformal mappings. J. Anal. Math.45, 181–206 (1985)

    Google Scholar 

  3. Gehring, F.W., Väisälä, J.: Hausdorff dimension and quasiconformal mappings. J. London Math. Soc.6, 504–512 (1973)

    Google Scholar 

  4. Granlund, S., Lindqvist, P., Martio, O.: Conformally invariant variational integrals. Trans. Am. Math. Soc.277, 43–73 (1983)

    Google Scholar 

  5. Heinonen, J., Kilpeläinen, T.:A-superharmonic functions and supersolutions of degenerate elliptic equations. Ark. Mat. (to appear)

  6. John, F.: On quasi-isometric mappings. I. Commun. Pure Appl. Math.21, 77–110 (1968)

    Google Scholar 

  7. John, F.: On quasi-isometric mappings. II. Commun. Pure Appl. Math.22, 265–278 (1969)

    Google Scholar 

  8. Martio, O.: A capacity inequality for quasiregular mappings. Ann. Acad. Sci. Fenn., Ser. AI 474, 1–18 (1970)

    Google Scholar 

  9. Martio, O., Rickman, S.: Measure properties of the branch set and its image of quasiregular mappings. Ann. Acad. Sci. Fenn., Ser. AI 541, 1–16 (1973)

    Google Scholar 

  10. Martio, O., Rickman, S., Väisälä, J.: Definitions for quasiregular mappings. Ann. Acad. Sci. Fenn., Ser. AI 448, 1–40 (1969)

    Google Scholar 

  11. Martio, O., Rickman, S., Väisälä, J.: Topological and metric properties of quasiregular mappings. Ann. Acad. Sci. Fenn., Ser. AI 488, 1–31 (1971)

    Google Scholar 

  12. Martio, O., Sarvas, J.: Injectivity theorems in plane and space. Ann. Acad. Sci. Fenn., Ser. A I4, 383–401 (1981)

    Google Scholar 

  13. Pommerenke, Ch.: Univalent functions. Göttingen Zürich: Vandenhoeck and Rupprecht 1975

    Google Scholar 

  14. Rado, T., Reichelderfer, P.V.: Continuous transformations in analysis. Berlin, Heidelberg, New York: Springer 1955

    Google Scholar 

  15. Reshetnyak, Yu.G.: Spatial mappings with bounded distortion. Sib. Mat. Zh.8, 629–658 (1967) (in Russian)

    Google Scholar 

  16. Reshetnyak, Yu.G.: Extremal properties of mappings with bounded distortion. Sib Mat. Zh.10, 1300–1310 (1969) (in Russian)

    Google Scholar 

  17. Rickman, S.: Quasiregular mappings, Proceedings of the Romanian-Finnish Seminar, Brasov 1969, Publishing House of the Academy of Romania, 1971, pp. 261–271

  18. Rickman, S.: Path lifting for discrete open mappings. Duke Math. J.40, 187–191 (1973)

    Google Scholar 

  19. Sarvas, J.: The Hausdorff dimension of the branch set of a quasi regular mapping. Ann. Acad. Sci. Fenn., Ser. A I1, 297–307 (1975)

    Google Scholar 

  20. Serrin, J.: Local behavior of solutions of quasi-linear equations. Acta Math.111, 247–302 (1964)

    Google Scholar 

  21. Tukia, P.: A quasiconformal group not isomorphic to a Möbius group. Ann. Acad. Sci. Fenn., Ser. A I6, 149–160 (1981)

    Google Scholar 

  22. Tukia, P., Väisälä, J.: Lipschitz and quasiconformal approximation and extension. Ann. Acad. Sci. Fenn., Ser. AI 6, 303–342 (1981)

    Google Scholar 

  23. Väisälä, J.: Minimal mappings in euclidean spaces. Ann. Acad. Sci. Fenn., Ser. AI 366, 1–22 (1965)

    Google Scholar 

  24. Väisälä, J.: Lectures onn-dimensional quasiconformal mappings. (Lecture Notes in Math., Vol. 229). Berlin, Heidelberg, New York: Springer 1971

    Google Scholar 

  25. Väisälä, J.: Modulus and capacity inequalities for quasiregular mappings. Ann. Acad. Sci. Fenn., Ser AI 509, 1–14 (1972)

    Google Scholar 

  26. Väisälä, J.: Uniform domains. Tôhoku Math. J.40, 101–118 (1988)

    Google Scholar 

  27. Vladimirov, V.S.: Equations of mathematical physics. New York: Dekker 1971

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Jyväskylä, Seminaarinkatu 15, SF-40100, Jyvaskylä, Finland

    O. Martio

  2. Department of Mathematics, University of Helsinki, Hallituskatu 15, SF-00100, Helsinki, Finland

    J. Väisälä

Authors
  1. O. Martio
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  2. J. Väisälä
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Martio, O., Väisälä, J. Elliptic equations and maps of bounded length distortion. Math. Ann. 282, 423–443 (1988). https://doi.org/10.1007/BF01460043

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