Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bers, L., F. John, and M. Schechter, Partial Differential Equations, Interscience Publishers, New York, 1964.
Beurling, A., and L. Ahlfors, The boundary correspondence under quasiconformal mappings, Acta Math. 96 (1956), 125–142.
Bojarski, B., and T. Iwaniec, Analytic foundations of the theory of quasiconformal mappings in ℝn, Ann. Acad. Sci. Fenn. Ser. A I Math. 8 (1983), 234–257.
Caffarelli, L., E. Fabes, and C. Kenig, Completely singular elliptic harmonic measures, Indiana Univ. Math. J. 30 (1981), 917–924.
Gehring, F. W., The L p-integrability of the partial derivatives of a quasiconformal mapping, Acta Math. 130 (1973), 265–277.
Granlund, S., P. Lindqvist, and O. Martio, Conformally invariant variational integrals, Trans. Amer. Math. Soc. 277 (1983), 43–47.
Granlund, S., P. Lindqvist, and O. Martio, F-harmonic measure in space, Ann. Acad. Sci. Fenn. Ser. A I Math. 7 (1982), 233–247.
Granlund, S., P. Lindqvist, and O. Martio, Phragmén-Lindelöf’s and Lindelöf’s theorems, Ark. Mat. 23 (1985), 103–128.
Heinonen, J., Boundary accessibility and elliptic harmonic measures, Complex Variables 10 (1988), 273–282.
Heinonen, J., and T. Kilpeläinen, A-superharmonic functions and supersolutions of degenerate elliptic equations, Ark. Mat. 26 (1988), 87–105.
Heinonen, J., and T. Kilpeläinen, Polar sets for supersolutions of degenerate elliptic equations, Math. Scand. (to appear).
Heinonen, J., and O. Martio, Estimates for F-harmonic measures and Øksendal’s theorem for quasiconformal mappings, Indiana Univ. Math. J. 38 (1987), 659–683.
Heinonen, J., T. Kilpeläinen, and O. Martio, Fine topology and quasilinear elliptic equations, Ann. Inst. Fourier (Grenoble) 39 2 (1989), 293–318.
Heinonen, J., T. Kilpeläinen, and O. Martio, Non-linear Potential Theory (to appear).
Heinonen, J., T. Kilpeläinen, and O. Martio, Harmonic morphisms for quasilinear elliptic partial differential equations. (to appear).
Iwaniec, T., Some aspects of partial differential equations and quasiregular mappings, Proceedings of ICM, Warsaw 1983, Warsaw, 1985, pp. 1193–1208.
Lehto, O., and K. I. Virtanen, Quasikonforme Abbildungen, Springer-Verlag, 1965.
Lindqvist, P., and O. Martio, Two theorems of N. Wiener for solutions of quasilinear elliptic equations, Acta Math. 155 (1985), 153–171.
Lindqvist, P., and O. Martio, Regularity and polar sets for supersolutions of certain degenerate elliptic equations, J. Analyse Math. 50 (1988), 1–17.
Martio, O., F-harmonic measures, quasihyperbolic distance and Milloux’s problem, Ann. Acad. Sci. Fenn. Ser. A I Math. 12 (1987), 151–162.
Martio, O., Counterexamples for unique continuation, Manuscripta Math. 60 (1988), 21–47.
Martio, O., Sets of zero elliptic harmonic measures, Ann. Acad. Sci. Fenn. Ser. A I Math. 14 (1989), 47–55.
Martio, O., Potential theoretic aspects of non-linear elliptic partial differential equations, Dept. of Math., Univ. of Jyväskylä, Report 44 (1989), 1–23.
Martio, O., Harmonic measures for second order non-linear partial differential equations, Function spaces, differential operators and non-linear analysis, L. Päivärinta, ed., Pitman Research Notes in Mathematics, 1989, pp. 271–279.
Martio, O., S. Rickman, and J. Väisälä, Definitions for quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I Math. 448 (1969), 1–40.
Martio, O., S. Rickman, and J. Väisälä, Distortion and singularities of quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I Math. 465 (1970), 1–13.
Martio, O., and J. Väisälä, Elliptic equations and maps of bounded length distortion, Math. Ann. 282 (1988), 423–443.
Maz’ya, V. G., On the continuity at a boundary point of solutions of quasi-linear elliptic equations, Vestnik Leningrad Univ. 3 (1976), 225–242. (English translation).
Morrey, C. B., On the solutions of quasilinear elliptic partial differential equations, Trans. Amer. Math. Soc. 43 (1938), 126–166.
Radó, T., Subharmonic Functions, Ergebnisse der Mathematik und Ihrer Grenzgebiete, Chelsea Publishing Company, 1949.
Reshetnyak, Yu. G., Space Mappings with Bounded Distortion, AMS Trans. of Math. Monographs vol. 73, 1989.
Rickman, S., Asymptotic values and angular limits of quasiregular mappings of a ball, Ann. Acad. Sci. Fenn. Ser. A I Math. 5 (1980), 185–196.
Rickman, S., Quasiregular mappings. (to appear).
Serrin, J., Local behavior of solutions of quasi-linear equations, Acta Math. 111 (1964), 247–302.
Tsuji, M., Potential Theory in Modern Function Theory, Maruzen Co., Tokyo, 1959.
Tukia, P., Hausdorff dimension and quasisymmetric mappings, Math. Scand. 65 (1989), 152–160.
Väisälä, J., Lectures on n-dimensional Quasiconformal Mappings, Lecture Notes in Mathematics 229, Springer-Verlag, 1971.
Väisälä, J., A survey of quasiregular maps in ℝn, Proceedings of ICM, Helsinki 1978, vol. 2, Helsinki, 1980, pp. 685–691.
Vekua, N., Generalized Analytic Functions, Pure and Applied Math. 25, Pergamon Press, 1962.
Vuorinen, M., Conformal Geometry and Quasiregular Mappings, Lecture Notes in Mathematics 1319, Springer-Verlag, 1988.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag
About this paper
Cite this paper
Martio, O. (1992). Partial differential equations and quasiregular mappings. In: Vuorinen, M. (eds) Quasiconformal Space Mappings. Lecture Notes in Mathematics, vol 1508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094238
Download citation
DOI: https://doi.org/10.1007/BFb0094238
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55418-9
Online ISBN: 978-3-540-47061-8
eBook Packages: Springer Book Archive