Acta Mathematica

, Volume 139, Issue 1, pp 155–184 | Cite as

The regularity of free boundaries in higher dimensions

  • Luis A. Caffarelli


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  1. [1].
    Agmon, S., Douglis, A. &Nirenberg, L., Estimates near the boundary of solutions of elliptic partial differential equations satisfying general boundary conditions.Comm. Pure Appl. Math., 12 (1959), 623–727.MathSciNetMATHGoogle Scholar
  2. [2].
    Brezis, H. &Kinderlehrer, D., The Smoothness of Solutions to Nonlinear Variational Inequalities.Indiana Univ. Math. J., 23, 9 (March 1974), 831–844.CrossRefMathSciNetMATHGoogle Scholar
  3. [3].
    Brezis, H. &Stampacchia, C., Sur la regularite de la solution d'inequations elliptiques.Gull. Soc. Math. France, 96 (1968), 153–180.MathSciNetMATHGoogle Scholar
  4. [4].
    Caffarelli, L., The smoothness of the free surface in a filtration problem.Arch. Rational Mech. Anal. (1977).Google Scholar
  5. [5].
    Caffarelli, L. &Riviere, N. M., On the smoothness and analyticity of free boundaries in variational inequalities.Ann. Scuola Norm. sup. Pisa, Sci. Fis. Mat., (Ser. IV), 3 (1976), 289–310.MathSciNetMATHGoogle Scholar
  6. [6].
    — The smoothness of the elastic-plastic free boundary of a twisted bar.Proc. Amer. Math. Soc., 63, (1977), 56–58.CrossRefMathSciNetMATHGoogle Scholar
  7. [7].
    Duvaut, G., Resolution d'un probleme de Stefan (Fusion d'un bloe de glace a zero degreé).C.R. Acad. Sci., Paris, sèr A.-B., 276 (1973), 1461–1463.MATHMathSciNetGoogle Scholar
  8. [8].
    Friedman, A., The shape and smoothness of the free boundary for some elliptic variational inequalities. To appear.Google Scholar
  9. [9].
    Friedman, A. &Kinderlehrer, D., A one phase Stefan problem.Indiana Univ. Math. J., 24 (1975), 1005–1035.CrossRefMathSciNetMATHGoogle Scholar
  10. [10].
    Kemper, J., Temperatures in several variables: Kernel functions, representations and parabolic boundary values.Trans. Amer. Math. Soc., 167 (1972), 243–261.CrossRefMATHMathSciNetGoogle Scholar
  11. [11].
    Kinderlehrer D., How a minimal surface leaves an obstacle.Acta Math., 130, (1973), 221–242.MATHMathSciNetGoogle Scholar
  12. [12].
    Kinderlehrer, D. & Nirenberg, L., Regularity in Free Boundary Problems.Ann. Scuola Norm. sup. Pisa Sci. Fis. Mat. To appear.Google Scholar
  13. [13].
    Lewy, H., On the reflection laws of second order differential equations in two independent variables.Bull. Amer. Math. Soc., 65 (1959), 37–58.MATHMathSciNetCrossRefGoogle Scholar
  14. [14].
    Lewy, H. &Stampacchia, G., On the regularity of the solution of a variational inequality.Comm. Pure Appl. Math., 22 (1969), 153–188.MathSciNetMATHGoogle Scholar
  15. [15].
    Nitsche, J. C. C., Variational problems with inequalities as boundary conditions or How to fashion a cheap hat for Giacometti's brother.Arch Rational Mech. Anal., 35 (1969), 83–113.CrossRefMATHMathSciNetGoogle Scholar
  16. [16].
    Serrin, J., On the Harnack inequality for linear elliptic equations.J. Analyse, 4 (1954–56), 292–308.MathSciNetCrossRefGoogle Scholar

Copyright information

© Almqvist & Wiksell 1977

Authors and Affiliations

  • Luis A. Caffarelli
    • 1
  1. 1.University of MinnesotaMinneapolisUSA

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