Hiroshima Mathematical Journal

On regularity of boundary points for Dirichlet problems of the equation $\Delta u=qu$ $(q\geq 0)$

Fumi-Yuki Maeda

Full-text: Open access

Article information

Source
Hiroshima Math. J., Volume 1, Number 2 (1971), 373-404.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1206137980

Digital Object Identifier
doi:10.32917/hmj/1206137980

Mathematical Reviews number (MathSciNet)
MR0320352

Zentralblatt MATH identifier
0273.31009

Subjects
Primary: 31C05: Harmonic, subharmonic, superharmonic functions
Secondary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]

Citation

Maeda, Fumi-Yuki. On regularity of boundary points for Dirichlet problems of the equation $\Delta u=qu$ $(q\geq 0)$. Hiroshima Math. J. 1 (1971), no. 2, 373--404. doi:10.32917/hmj/1206137980. https://projecteuclid.org/euclid.hmj/1206137980


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References

  • [1] N. Boboc, C. Constantinescu and A. Cornea, On the Dirichlet problem in the axiomatic theory of harmonic functions, Nagoya Math. J., 23 (1963),73-96.
  • [2] M. Brelot, Lectures onpotential theory,Tata Inst. of F.R., Bombay, 1960.
  • [3] M. Brelot, Sur un theoremede nonexistence relatif a Vequation u=c (M)u, Bull. Sci. Math., 56 (1932), 389-395.
  • [4] M. Brelot, Etude a la frontiere de la solution du probleme de Dirichlet generalise relatif a Vequation u =cu+f; c(M)^0, \f{M) borne, Rend. 1st. Lombardo, 65 (1932),119-128.
  • [5] M. Brelot, Sur Failure a lafrontiere des integrates bornesde u = c (M)u(c^O), Ibid., 433-448.
  • [6] G. Constantinescu and A. Cornea, Ideate Rnder Riemannscher Flchen, Springer-Verlag, Berlin- Gottingen-Heidelberg, 1963.
  • [7] C. Constantinescu and A. Cornea, Compactifications of harmonic spaces, Nagoya Math. J., 25 (1965), 1-57.
  • [8] M. Glasner, Dirichlet mappings of Riemannian manifolds and the equation u = Pu, J. DifF. Eq., 9 (1971), 390-404.
  • [9] L.L. Helms, Introduction to potential theory, Wiley-Interscience, New York-London-Sydney- Toronto, 1969.
  • [10] R. -M. Herve, Recherchesaxiomatiques sur la theorie des functions surharmoniques et du potentiel, Ann. Inst. Fourier, 12 (1962), 415-571.
  • [11] R. -M. and M. Herve, Lesfunctions surharmoniques associees un oprateur elliptique du second ordre a coefficients discontinus, Ibid., 19-1 (1969),305-359.
  • [12] P.A. Loeb, An axiomatic treatment of pairs of elliptic differential equations,Ibid., 16-2 (1966), 167- 208.
  • [13] P.A. Loeb and B. Walsh, A maximal regular boundary for solutions of elliptic differential equations, Ibid., 18-1 (1968),283-308.
  • [14] F-Y. Maeda, Boundaryvalueproblems for the equation u--qu=0 with respect to an ideal boundary, J. Sci. Hiroshima Univ., Ser. A-I, 32 (1968),85-146.
  • [15] F-Y. Maeda, Comparisonof the classes of Wiener functions, Ibid., 33 (1969),231-235.
  • [16] F-Y. Maeda, Harmonic and full-harmonic structures on a differentiable manifold, Ibid., 34 (1970), 271-312.
  • [17] K. Miller, Barriers on cones for uniformly elliptic operators, Ann. di Mat., Ser. 4, 76 (1967),93-105.
  • [18] G. Prodi, Sul primo problema at contorno per equazionia derivate parziali ellittiche o paraboliche, con seconde membro illimitato sullafrontier a, Rend. 1st. Lombardo, 90 (1956), 189-208.
  • [19] G. Stampacchia, Le probleme de Dirichlet pour les equations elliptiques du secondordre a coefficients discontinus,Ann. Inst. Fourier, 15-1 (1965), 189-258.
  • [20] M. Tsuji, Potential theory in modern function theory, Maruzen, Tokyo, 1959.
  • [21] S. Warschawski, Uber des Randerhalten der Ableitung der Abbildungsfunktion bei konformer Abbildung, Math. Zeit., 35 (1932),321-456.
  • [22] K. -O. Widman, Inequalities for the Green function and boundary continuity of gradient of solutions of elliptic differential equations, Math. Scand., 21 (1967), 17-37.