Acta Mathematica

A minkowski problem for electrostatic capacity

David Jerison

Full-text: Open access

Dedication

Dedicated to my father, Meyer Jerison

Note

The author was partially supported by NSF Grants DMS-9106507 and DMS-9041355.

Article information

Source
Acta Math. Volume 176, Number 1 (1996), 1-47.

Dates
Received: 2 January 1995
Revised: 19 September 1995
First available in Project Euclid: 31 January 2017

Permanent link to this document
http://projecteuclid.org/euclid.acta/1485890918

Digital Object Identifier
doi:10.1007/BF02547334

Zentralblatt MATH identifier
0880.35041

Rights
1996 © Institut Mittag-Leffler

Citation

Jerison, David. A minkowski problem for electrostatic capacity. Acta Math. 176 (1996), no. 1, 1--47. doi:10.1007/BF02547334. http://projecteuclid.org/euclid.acta/1485890918.


Export citation

References

  • Borell, C., Capacitary inequalites of the Brunn-Minkowski type. Math. Ann., 263 (1983), 179–184.
  • Bonnesen, T. & Fenchel, W., Theory of Convex Bodies, BCS Associates, Moscow, ID, 1987 (translation from German).
  • Carleson, L., Selected Problems on Exceptional Sets, Van Nostrand, Princeton, NJ, 1967.
  • Caffarelli, L. A., Interior a priori estimates for solutions of fully non-linear equations. Ann. of Math., 131 (1989), 189–213.
  • —, A localization property of viscosity solutions to the Monge-Ampère, equation and their strict convexity. Ann. of Math., 131 (1990), 129–134.
  • —, Interior W2,p estimates for solutions of the Monge-Ampère equation. Ann. of Math., 131 (1990), 135–150.
  • —, Some regularity properties of solutions to the Monge-Ampère equation. Comm. Pure Appl. Math., 44 (1991), 965–969.
  • Caffarelli, L. A., Jerison, D. & Lieb, E. H., On the case of equality in the Brunn-Minkowski inequality for capacity. To appear in Adv. in Math., 1996.
  • Caffarelli, L. A., & Spruck, J., Convexity properties of solutions to some classical variational problems. Comm. Partial Differential Equations, 7 (1982), 1337–1379.
  • Cheng, S.-Y. & Yau, S.-T., On the regularity of the solution of the n-dimensional Minkowski problem. Comm. Pure Appl. Math., 29 (1976), 495–516.
  • Dahlberg, B. E. J., Estimates for harmonic measure, Arch. Rational Mech. Anal., 65 (1977), 275–283.
  • Gabriel, R. A result concerning convex level surfaces of the Green's function for a 3-dimensional convex domain. J. London Math. Soc., 32 (1957), 286–294 and 303–306.
  • Garabedian, P. R. & SChiffer, M., On estimation of electrostatic capacity. Proc. Amer. Math. Soc., 5 (1954), 206–211.
  • Guzmán, M. deDifferentiation of Integrals inRn. Lecture Notes in Math., 481. Springer-Verlag, Berlin-New York, 1975.
  • Jerison, D. Prescribing harmonic measure on convex domains. Invent. Math., 105 (1991), 375–400.
  • Jerison, D. & Kenig, C. E., Boundary behavior of harmonic functions in nontangentially accessible domains. Adv. in Math., 46 (1982), 80–147.
  • — The logarithm of the Poisson kernel of a C1 domain has vanishing mean oscillation. Trans. Amer. Math. Soc., 273 (1982), 781–794.
  • John, F. & Nirenberg, L. On functions of bounded mean oscillation. Comm. Pure Appl. Math., 14 (1961), 415–426.
  • Kellogg, O. D., Foundations of Potential Theory, Dover, New York, 1929.
  • Poincaré, H., Figures d'équilibre d'une masse fluide. Paris, 1902.
  • Stein, E. M., Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, NJ, 1970.