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Regularization of mixed second-order elliptic problems

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Abstract

It is shown that weak solutions of mixed elliptic problems are Hölder continuous of any order less than 1/2 and that they possess higher regularity in non-critical directions.

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Bibliography

  1. S. Agmon,The L p approach to the Dirichlet problem, Ann. Sc. Norm. Sup. Pisa13 (1959), 405–448.

    MathSciNet  Google Scholar 

  2. -----,Unicité et convexité dans les problèmes différentiels, University of Montreal Press, 1966.

  3. L. Arkeryd,On the L p estimates for elliptic boundary problems, Math. Scan.19 (1966), 59–76.

    MathSciNet  Google Scholar 

  4. G. Fichera,Alcuni recenti sviluppi della teoria di problemi al contorno, Atti Convegno Internaz. sulle Eq. Der. Parz. 1954 (Trieste). Cremonese, Roma.

  5. L. Hörmander,Linear partial differential operators, Springer, Berlin, 1963.

    MATH  Google Scholar 

  6. J. I. Lions, and E. Magenes,Problemi ai limiti non omogenei, III, IV, V. Ann. Sc. Norm. Sup. Pisa15 (1961), 39–101; 311–326;16 (1963) 1–44; VI. Jour. d’Analyse Math.11 (1963), 165–188.

    Google Scholar 

  7. J. L. Lions and J. Peetre,Sur une class d’espaces d’interpolation, Inst. Hautes Etudes Sci.19 (1964), 5–68.

    Article  MATH  MathSciNet  Google Scholar 

  8. E. Magenes,Spazi di interpolazioni ed equazioni a derivate parziali, Proc. of the Italian Math. Union 7th Congress, Geneva, 1963.

  9. J. Peetre,Espaces d’interpolation et théorème de Soboleff, Ann. Inst. Fourier16 (1966), 279–317.

    MATH  MathSciNet  Google Scholar 

  10. M. Schechter,On L p estimates and regularity, I. Amer. Jour. of Math.85 (1963), 1–13, II. Math. Scand.13 (1963), 47–69. III. Ricerche di Matematica8 (1964), 192–206.

    Article  MATH  MathSciNet  Google Scholar 

  11. E. Shamir,Une proprieté des espaces H s,p, C. Acad. Sci. Paris255 (1962), 448–449.

    MATH  MathSciNet  Google Scholar 

  12. —————,Multipliers of Fourier transforms in a half-space, Bull. Amer. Math. Soc.71 (1965), 165–167.

    Article  MATH  MathSciNet  Google Scholar 

  13. —————,Elliptic Systems of Singular Integral Operators, I.The half-space case, Trans. Amer. Math. Soc.,127 (1967), 107–124.

    Article  MATH  MathSciNet  Google Scholar 

  14. G. Stampacchia,Problemi al contorno, con dati discontinui, dotati di soluzioni Hölderiane, Annali di Matematica51 (1960), 1–37.

    Article  MATH  MathSciNet  Google Scholar 

  15. E. M. Stein,The characterization of functions arising as potentials I, II, Bull. Amer. Math. Soc.67 (1961), 102–104;68 (1962), 577–582.

    Google Scholar 

  16. A. P. Calderón,Integrales singulares y sus applicaciones, Univ. of Buenos Aires, 1960.

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Shamir, E. Regularization of mixed second-order elliptic problems. Israel J. Math. 6, 150–168 (1968). https://doi.org/10.1007/BF02760180

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