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Two theorems of N. Wiener for solutions of quasilinear elliptic equations

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References

  1. Beurling, A. &Ahlfors, L. V., The boundary correspondence under quasiconformal mappings.Acta Math., 96 (1956), 125–142.

    MathSciNet  Google Scholar 

  2. Brelot, M., Familles de Perron et problème de Dirichlet.Acta Sci. Math. (Szeged), 9 (1939), 133–153.

    MATH  MathSciNet  Google Scholar 

  3. —,Éléments de la théorie classique du potentiel (2ème édition). Centre de Documentation Universitaire Paris, Paris 1961.

    Google Scholar 

  4. Gariepy, R. &Ziemer, W. P., A regularity condition at the boundary for solutions of quasilinear elliptic equations.Arch. Rational Mech. Anal., 67 (1977), 25–39.

    Article  MathSciNet  Google Scholar 

  5. Gehring, F. W., Symmetrization of rings in space.Trans. Amer. Math. Soc., 101 (1961), 499–519.

    Article  MATH  MathSciNet  Google Scholar 

  6. Granlund, S., Lindqvist, P. &Martio, O., Conformally invariant variational integrals.Trans. Amer. Math. Soc., 277 (1983), 43–73.

    Article  MathSciNet  Google Scholar 

  7. —,F-harmonic measure in space.Ann. Acad. Sci. Fenn. Ser. A I Math., 7 (1982), 233–247.

    MathSciNet  Google Scholar 

  8. Granlund, S., Lindqvist, P. & Martio, O., Note on the PWB-method in the non-linear case. To appear.

  9. Littman, W., Stampacchia, G. &Weinberger, H. F., Regular points for elliptic equations with discontinuous coefficients.Ann. Scuola Norm. Sup. Pisa Ser. 3, 17 (1963), 43–77.

    MathSciNet  Google Scholar 

  10. Loewner, C., On the conformal capacity in space.J. Math. Mech., 8 (1959), 411–414.

    MATH  MathSciNet  Google Scholar 

  11. Martio, O. &Sarvas, J., Density conditions in then-capacity.Indiana Univ. Math. J., 26 (1977), 761–776.

    Article  MathSciNet  Google Scholar 

  12. Mazja, V., On the continuity at a boundary point of solutions of quasilinear elliptic equations (Russian).Vestnik Leningrad. Univ. Math., 13 (1970), 42–55.

    MATH  MathSciNet  Google Scholar 

  13. —, A letter to the editor (Russian).Vestnik Leningrad. Univ. Math., 1 (1972), 160.

    Google Scholar 

  14. Püschel, W., Die erste Randwertaufgabe der allgemeinen selbstadjungierten elliptischen Differentialgleichung zweiter Ordnung für beliebige Gebiete.Math. Z., 34 (1931/32), 535–553.

    Article  Google Scholar 

  15. Sarvas, J., Symmetrization of condensers inn-space.Ann. Acad. Sci. Fenn. Ser. A I Math., 522 (1972), 1–44.

    Google Scholar 

  16. Väisälä, J.,Lectures on n-dimensional quasiconformal mappings. Lecture Notes in Math., 229. Springer-Verlag, Berlin and New York, 1971.

    Google Scholar 

  17. Wiener, N., Certain notions in potential theory.Journal of Math. and Phys., Massachusetts Institute of Technology, 3 (1924), 24–51.

    MATH  Google Scholar 

  18. —, The Dirichlet problem.Journal of Math. and Phys., Massachusetts Institute of Technology, 3 (1924), 127–146.

    MATH  Google Scholar 

  19. —, Note on a paper of O. Perron.Journal of Math. and Phys., Massachusetts Institute of Technology, 4 (1925), 21–32.

    MATH  Google Scholar 

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Lindqvist, P., Martio, O. Two theorems of N. Wiener for solutions of quasilinear elliptic equations. Acta Math. 155, 153–171 (1985). https://doi.org/10.1007/BF02392541

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